All right, welcome back. And today it's all about the animation contest, the 100 frame animation contest or challenge whatever you want to call it, whatever I call it. And today's clip is to let you know that Friday the 13th, creepy Friday the 13th I am going to announce the topic and then you have one week until Friday the 20th end of day to submit your 100 frame submission. Now, what is this? What am I talking about? At the end of each semester at the Academy I do a 100 frame assignment. So basically, we are in the room, we come up with all kinds of topics, then we vote on that one topic, that will be the defining topic for the animation. Now, the animation is only 100 frames long, you can do shorter, I guess, if you want to, but not longer. So it's 100 frames only, you can add sound if you want, you can add music if you want, whatever you want to do to kind of enrich this sounds and whatever you want. Ultimately, it's 100 frames of just animation. This could be one shot, this could be multiple shots, whatever it is, just not longer than 100 frames. This can be in 2D, 3D, stop motion, sand, paper, whatever you want to do, right? It's something that's animated 100 frames based on that topic. And then that Friday the 20th, all the submissions, I'm going to collect them, show them a couple friends of mine, we're going to vote on the subjectively best one that we like that fits that topic. And then the winner gets $100, either just bam, PayPal, or you can pick something from Amazon, I'll send it to you, but the winner will get that the submissions will be from people online and also my students at the Academy of Art. So it's kind of a big group of people that will submit and I will have all the links that you need with explanations, examples, previous submissions, all that good stuff. If you want to wrap your head around on what is going on here to check it out in the description, all the info is there. So Friday the 13th, I will announce the topic on this channel on Twitter, everywhere. And then Friday the 20th, end of day. So midnight, San Francisco time will be the end of all the submissions. And I will also have in the description, the email is going to be contest at spongel.com. But again, all the info is in the description. So open up that little box and check it all out. If you have any questions, comments are open, of course, let me know whatever you need to have in terms of clarifications or help whatever it is. But once the topic is known, I will not help it will just be you animating and being awesome and submitting your shop. And speaking of awesome. Also, and, and calm on love the show love the crew gear, cool designs, cool colors. Love it. The spoiled perks of working at ILM. But anyway, has nothing to do with the context. But I'm wearing this today as I thought, let me just record a clip with this and go, yeah, actually, if you have seen Mandalorian, and you're watching it on Disney Plus, let me know in the comments, what do you think would be cool to know your thoughts on that show. But anyway, this is about the contest. So that's it. I'm going to keep my mouth shut now and stop everything. And good luck with your submission.


Hey guys, so this is the brand new lens by Tamron, it's the 17x28mm wide angle f2.8 lens for Sony E-mount cameras. It's the successor to the Tamron 28-75mm lens, but is even shorter and lighter than its predecessor. In this video I'm going to give you an overview of its capability with sample photos, videos, autofocus and a lot more, so let's just get straight into it. Now, starting off with the design and build, it's not the smallest lens out there, but for a full frame lenses, it's definitely the lightest and a very compact lens. It feels like a cheaper build than most lenses out there because it's made of durable plastic rather than solid metal, but Tamron saves costs and returns that cost saving back to the customers at huge discounts, which is why it comes in at a reasonable £899 as compared to the high end full frame lenses out there. The lens no longer extends when zooming, instead the zoom takes place right in front of the focus ring. The length of the lens is 99mm and it has the same diameter of the previous Tamron 28-75mm lens which is approximately 73mm. Now let's take a look at some photos and see how the pictures came out under the auto setting of my Sony a7 III. As with most wide angle lenses, they are really great at landscape photography, capturing everything and more that you need. Now taking these sample pictures at 17mm wide angle, I have to say I was quite surprised at how super sharp the pictures were at full aperture, even from corner to corner. Nonetheless, you can see there is real clarity, sharp colours and is still excellent for demanding applications such as Final Cut Pro or Adobe editing programs. Now just to show you how much of a difference in zoom there is between the 17mm and the 28mm focal length, here is some comparisons I've put together. All the pictures were taken on auto setting and I've displayed the aperture f-stops that were generated. One of the main reasons that people buy DSLR cameras is for the awesome portrait photography that they can produce. So let's now take a look at some close up photos and see how soft of a background blur you can see. Of course with a 17mm at f2.8 you don't get a very soft almost impressionistic background but on a full-frame camera you do get a gradient in sharpness. Take a look at how soft the background is as I get closer to the camera in these shots which I've set at 24mm focal length and actually I was pleasantly surprised it has maintained a bokeh effect quite well and has a soft depth of field without bleeding over the edges of my body in any way. In these other close up photos I've taken them all at 17mm to see the gradient in the background using very wide angle shots and you will see that even then it makes that gradient look soft and organic. An excellent job by Tamron on this front but if you take the same pic at both 17 and 28mm keeping the same distance you can definitely see the difference in sharpness and gradient blur in the background as you can see from the picture here. Next I played around with the autofocus on movie recording mode to test the speed and clarity of autofocus. The Tamron RXD which stands for Rapid Extra Silent Stepping Drive provides a motor that is quiet fast and accurate. In this first clip I was walking towards the camera to see if I get out of focus at any point and it held up really well and I was on focus the whole time. Now to test the speed of the autofocus I put my hand in front of the camera at different speeds and can see it took around two seconds to register the focus which was my third attempt in this clip. Again on the speed when you pan away from the close-up object the autofocus will be very fast but when trying to focus back onto the close-up object it takes a second or two to pick up the focus as you can see here. And finally this didn't work 100% of the time here I panned away it focused on the distance and when panning back it didn't capture the close-up focus until I stepped back a little and moved into the pole again but for the majority of the situations it did a great job. The Sony A7 cameras have great stabilization but this Tamron lens has no stabilization inbuilt into it. As you can see from these clips of me walking and then running it is very shaky so ideally you'd have to get a gimbal so that you can record smooth cinematic footage for this lens and this camera. In conclusion I would have to say that this lens has more pros than cons with the pros being that it's very light bright compact has an internal zoom has fast autofocus and is weatherproof and it's a lot cheaper than a lot of full-frame lenses on the market right now. The pictures are very sharp and great for landscape and architecture photography and you can actually get some very good portrait photography with this lens as well. The cons on the other hand are that it has no stabilization the lens is plastic so if you do drop it you might damage it more easily there are no switches on the lens and it has a slightly shorter range than comparable lenses. So I hope you found this review useful guys I have another Tamron review video coming out very soon it's for nighttime photography and video recording just to give you an idea of actually how well it works in very low lighting conditions so make sure you hit that subscribe button to not miss that. If you have any questions let me know below check out the relevant purchase links in the description and I will catch you guys at the next one take care


Former governor-general of St. Lucia, Excellency D'Empollet-Louisie, recently took the COVID-19 vaccine and encourages all to do the same to protect themselves, their families and others. Excellency D'Empollet-Louisie spoke on her personal decision to get vaccinated and the experience of doing so. It was a breeze. I've been vaccinated before, smallpox, and I think I was vaccinated for malaria once when I traveled to Africa.  I have to admit I was a bit apprehensive in the beginning, but with time and with, you know, getting myself, well, I wouldn't say educated, but reading about it, weighing the pros and the cons. I say, you know, if I have trusted doctors for this, for the past 70 years, I think I can trust them still. The former governor-general says although taking the COVID-19 vaccine is voluntary and people may have fear, she would definitely encourage other individuals to take the leap of faith and get vaccinated.  I feel well, I think, in the most part by, you know, what people read, you know, particularly on social media, contradictions, even among health professionals, so people are questioning. But I would say, you know, as I said before, you trust the doctor if the medication he gives you. You don't ask, you know, why is that good for your body, you know?  The Ministry of Health encourages individuals to pre-register for the COVID-19 vaccine via the online platform at hmi.govt.lc or at your nearest Community Wellness Centre. Reporting from the Communications Unit of the Ministry of Health and Wellness, I am Fonal Neptune.


All right, awesome. Cool. Hi, everyone. Today, we're going to be talking about applying observability to machine learning, so figuring out how you can use observability to debug your machine learning models that are deployed on the edge. So first, just as an introduction, Natalie and I, we are principal engineers at New Relic, and we work primarily on Pixi, which is an open source CNCF sandbox project for Kubernetes observability. And you'll learn a little bit more about Pixi later on in our talk. So why is this important? We see today that a bunch of products and software are moving their ML to the edge. So for example, here you see with Cruz, the self-driving car, it's collecting a bunch of information using its sensors, cameras to figure out, am I driving in the lane correctly? Am I about to hit something in obstacle? And it collects all that information and does it locally. So it stores it locally and then runs some inference on it to figure out what action it should do next. And then similarly, you have the Amazon Echo, and that does the same thing. It collects input from the environment, whatever you're saying at the time in your home, and tries to figure out, should I do something with this information? And what does this exactly look like? So in the traditional model that you see on your left, before a lot of how things were being done was all these sensors were collecting information, and then in order to make an inference on it, it'll send it off to some cloud. This model is running in the cloud. It receives that information and then sends back, OK, here's what you should do with this. And then now, as things are moving towards the edge, you're seeing a lot more of this sensor is collecting this information. It's storing it potentially in memory, and then it runs the model directly on the device itself. Show me the flip for you. So there's a lot of benefits to this, right? You can see immediately here from this picture, you get a lot less network bandwidth in egress, especially if your sensor is collecting tons of information. Now you're not sending out to some other cloud that you potentially don't even own. And so that's really nice because you get the data and you can immediately start processing running your models on it. And then second of all, the nice thing about it is you get some really good security privacy benefits, right? So think about the Amazon Echo case. Your Echo is sitting on your counter, and it feels a little bit weird to be like, oh, it's listening to me and sending all whatever I'm saying all the way directly to Amazon, right? It's nice to think about it's like, OK, it's actually doing edge compute. Whatever I'm saying, it's storing it locally. Probably expiring it out after some point because that's a ton of data that it's collecting. And all of it is just stored within the edge device itself. And then finally, there's scalability. So before, if you have millions of connected devices and all of these are streaming their data to your cloud, you're going to have to be able to handle all this input from a bunch of these different devices. But now all these models are running individually on the device itself. And so they're just responsible for dealing with their own set of inferences. So how does this actually look like? How do you start to go and deploy your models to your edge devices? And how it usually happens is that the first part is pretty much the same, right? You need to go and you train your model. You have a bunch of training data. You go and you make sure you tune all your parameters and make sure your accuracy is correct. Like you have an image classification. You're trying to classify what kind of dog breed is this. You train this in the cloud. And you ensure it's like, OK, any input I give it, it looks about right. And then you go and you can deploy these to all these different edge devices. So I wanted to make it very clear that all these are just potentially different hardware environments. So I just made these boxes of the edge devices different colors. Because one could be an iPhone. One could be an Android device. So it's just very clear that these models are now going to a very different set of environments. And what actually can happen here? What could go wrong? It works perfectly in the cloud. And keep in mind that your cloud, it has as many resources as you want to give it. You can give it as much memory you want. You give it as much CPU that you want. And as long as you're willing to pay. But then now you're going to these edge devices. And like I mentioned before, you have phones. But you might be deploying to just some little thing, running a sensor or something.  So the first case up on top is you've deployed to your edge device. And then things seem to run. But then you get the completely wrong results. You're noticing a huge drop in accuracy. So before maybe when you had 80, 90% accuracy, you're seeing that your model that's been deployed somewhere else is giving you maybe even 30% accuracy. And the second case where something could go wrong is your model seems to run fine. It's giving you the right inferences. But it's taking a really, really long time. And so it's like, OK, it used to work. Now it doesn't. What can I do to go and debug this? And I think a lot of the things that we turn to, I'm sure many people here are familiar with it, are like, I need to figure out how to solve this problem. I'm going to go and just put a bunch of print statements and just figure out where exactly in this pipeline are things going wrong. And obviously that's a very tedious problem because there's especially in a deep learning model, there's a lot of stuff going on in there, right?  You have to make sense of all that information. And that is where MLXray comes in. So MLXray is a project that came out of a Stanford research project. So huge credits goes to all these people that I've listed on the bottom who came up with the original idea for MLXray and all the great work that they've done so far on it. And essentially what MLXray is, is that it's an end-to-end framework for debugging your cloud-to-edge deployment. And let's dive a little bit into more about what that actually means. So first, MLXray gives you this API. And you basically invoke that API.  So up on top, we have an example of the Python API. You start the inference. You stop the inference using the MLXray API. And during each part in your model pipeline, it just records tons of information. So it's like the pre-processing step, the individual layers down to the final output that it gets in the end. So you don't have to go in and actually add whatever logging that you yourself want. So what kind of information does it get?   So what are the inputs and outputs of your model? And then for each individual layer inside your model pipeline, it also gets the input and output of that. And for the case where things start running very slowly, it will track your end-to-end latency for running the entire inference, but also in between each layer itself. And just resource information. So it's like, what was the memory when my model was running? And for devices like Android, it also collects just other sensor information. So it's like, your Android knows how it's rotated, what the lighting conditions are like. And that just helps give more context to just how the model is running on your device. And you can go ahead and use the MLXray API to just add whatever other fields you might want to log. So more information that you might want to collect that are specific to your model itself. But now you have all this data coming in, right? So you're like, all right, cool, I've instrumented my stuff. But what do you do with it? Now you're like, OK, I know it takes this long. I know that at this point, my output looks like this. What am I supposed to do now? And so the idea behind MLXray is that you compare this to a reference pipeline. So you have your model that you've trained in the cloud. You know, this is your baseline model. This thing runs the best that you can imagine, the best accuracy that you can get. It runs at the speed that you want. And so what you do here is you collect logs from that baseline model. And then you have the one that you've deployed to your edge device. You collect the logs from that one. And essentially, you combine them together to figure out, what are the differences here? And that's what we call a debug report. So you compare the differences and try to figure out where exactly in my model are things going wrong. And what does this flow kind of look like when you're debugging? So the first is in accuracy validation. Is the model that's deployed on your edge device, is it doing as well as the cloud model that you originally trained? And so if it is, that's great. Maybe they have comparable performance. And you're done. It's like, all right, great. I've deployed to this Android. I'm good. Everything looks good. I can move on to whatever the next device I want to deploy to. But a lot of the time, it's going to be like, OK, no. My accuracy has dropped a lot. And so that's when you look into the accuracy or the output between each layer. And what you might see here is like, oh, OK, this particular layer, the output is very, very different from the output that I was getting in my baseline reference model. And so then there you can go and look into, OK, maybe I have some pre-processing issues. Maybe there's something wrong with the weights and biases in this model when you try to quantize it so that it runs better on an edge device. So that gives you indication about just which layer you should actually look into. And then finally, MLXray has this thing called custom assertion checks. And so what actually happens there is that you can tell MLXray, as you're running through my model and collecting all these logs, just run some assertions that I know always need to be the case so that if it fails, I know there's already something in my pipeline that is wrong. And so an example of this is, going back to the lane detection case, you know that when it detects a lane in a picture, it has to be this wide, for example. And so you can add an assertion to be like, whenever you detect a lane, always make sure it's this width. And then if it isn't, then it will trigger a failure and can be like, oh, OK, so there's something wrong potentially here. And so how Natalie and I kind of got involved in MLXray, so all the work I just presented before was work that was done by those people I mentioned at the Stanford Research Group, was that we got in contact with these people and we found there's a lot of limitations with MLXray that Pixi, which we'll talk about in a little bit, could potentially solve. So the first is you have to make code changes to enable this instrumentation. It's not a lot of code, right?  So it's like, you have to remember to go and add that in, you have to remember to take it out because whenever you're ready to finally deploy to prod, you don't wanna keep just logging all this information all of the time. And it has a slight performance impact sometimes as well, plus memory because now you're keeping all of this data in a log stored on your device so you can pull it out later to analyze it. And the third thing, which I didn't show as much, but there's just not a lot of ways to visualize this data. So MLXray, it gives you an API for collecting the data and parsing it, and it gives you some simple operation so it's like, okay, I can plot these two different like layer accuracies against each other, but there's no way to actually go and like play around with this data and try exploring different correlations. And so then that's where Pixi comes in. So I will hand that over to Natalie to explain what that's about. All right, thanks, Michelle. So as Michelle said, you know, as contributors to the Pixi project, we were really inspired when we saw what MLXray could do. And what we wanted to do is try to take some of its concepts and see how we could use Pixi, which is an observability platform for Kubernetes to apply some of these concepts in a Kubernetes native environment. So just a little bit about Pixi before we jump into the demo. Pixi provides auto telemetry to your Kubernetes cluster using EBPF so it can automatically collect a lot of data from your application without any code changes. Pixi runs on the edge, which makes it a good, you know, option for edge-based deployments because the compute and the data collection and all that stuff actually lives on the node on which it's collected. And then finally, Pixi has a very customizable interface so that allows us to build custom dashboards for specific use cases that we have. And as she said before, Pixi is a CNCF sandbox project, totally open source, so anyone can use it. So I think the way we think about Pixi is progressive instrumentation, which means you start with a baseline of a certain amount of visibility into your system and you can extend that visibility in areas that you're interested in. So Pixi, right out of the gate, has things like resource utilization, flame graphs showing which functions are taking a long time in your application. It shows the raw requests in and out of your application. But we also have the ability to, once Pixi's deployed in the cluster, to add additional user-specific instrumentation for your application. So we can use Uprobes, which is a user-space BPF probe to trace particular functions in your application that you're interested in without requiring a redeploy or anything like that. You can write custom scripts and custom dashboards and soon it's gonna support things like supporting arbitrary data sources from open telemetry ingest and things like that. In the diagram below, we just have an example of how Uprobe works in your system. So you can say, I'm going to trace this particular function, the function will then run, and then the Uprobe will actually read the values in and out of the application, or in and out of the function, if that's what you're telling it to trace. You can collect things like latency, arguments, return values, and things like that using Uprobes. So next I'll show a demo. This is just the beginning of using Pixi to apply some of the ML X-ray concepts, but I wanted to show it on an application and show ML observability on the edge using Pixi. So, okay, well, I was warned that this might happen. It's back, okay, great. So I just made a quick little GitHub project to run a Kubernetes object detection, so you can check it out if you want to test it out yourself. I have that application running on my Kubernetes cluster. So this is the Pixi UI. You can see that it's showing me the traffic between different applications in my cluster, things like the nodes and the namespaces. And specifically what I'm interested in is this model server, which is running my TensorFlow application, which is an image classifier. So right off the bat we can see things like, what's the CPU usage? What are the containers that are running? What are the processes? Bites in and out, things like that.  And what I want to do is I'm going to apply custom Uprobes using a Pixel script, and that's going to allow me to trace model execution in terms of the number of times that it's run, and also the latency of the model execution. So I'm going to go to my scratch pad. I'm starting some load over here. We're going to need to re-forward this port, taking a little bit of time. Demo gods be with me. But basically what I'm going to try to do here is say, hey, Pixi's already collecting a lot of information about my application, but I specifically want to trace particular functions that are running my model. So that's the goal of what I'm about to do. Still struggling, I'll try. I do have a video of this if it fails to work. Do you think I should go to the video? Or do you think I should? Okay, stand by while we, I just have to pull this out of my files. So as you can see, kind of the same thing that we showed earlier, I'm just going to jump ahead to the part where I'm going to deploy the probe. So basically, as I said, we're basically going to instrument this application using a custom script. This is deploying Uprobes that I have written in BPF Trace. And it's basically going to show me the latency and the number of times this model was executed. Over time in my cluster, without any redeploys. So by using things like this, we're able to add additional observability into our models once they're deployed when they're running on Kubernetes. So the trace point is being deployed. And soon we'll see a plot of latency as well as number of invocations over time for my model. Just giving it a little time to collect some additional data. Okay, there we go. We can see model requests over time. That's the top chart. And then the model latency. We have the P50, P90, and P99 for how long the model is taking to execute. So you might think, okay, it's taking about a second to execute, that might be a little bit long. I need more information about what's happening. I need to debug this and figure out where the bottleneck is. So I mentioned before that Pixi has flame graphs that it captures about the most CPU intensive functions that your application's running. It might be a little hard to see here, but you can basically see the entire call stack of what's running. And what I'm gonna discover looking at this is that most of the time here is spent parsing JSON and serializing JSON. It's not actually spent on the model itself. And this is a really common problem. Without the ability to attribute the latency, you actually might blame the model when it isn't actually the model's fault. But there is a particular part in here that it's gonna highlight soon, which is basically a layer of the model that is taking a really long time in comparison to what we'd expect. And that's underneath this parent function. We can see the different ops that are running, the gather op, a king cat op. And then finally, we're gonna see a non-max suppression op. Now, this is a particular operation that we expect to be really, really fast. It's basically just saying, I have a bunch of different bounding boxes. Which ones are the ones that I should actually output? So, it's kind of a surprise that this would even show up at all, especially in comparison to the other ops. But as we've established, we have the ability to do custom tracing of whatever function that we want. So, what I'm gonna do here in the last part of the video is basically trace arguments to this non-max suppression operation and try to figure out, based on the arguments that it's receiving, why it might be taking a long time. So, I'm gonna run another script. And it's basically going to trace that particular operation. And let's see if we can figure out a little bit about why it's taking longer than we think. Okay, it's a little hard to see here because of the small tax. But what we see is that there are actually thousands of bounding boxes being passed into this function. 2000, in fact. That is a lot higher than I might expect from my reference pipeline. So, this has allowed me to get to the part of the issue, which is why is this particular layer of my model slow? It's because it's receiving an outsize input. It's an input that we wouldn't actually expect. So, we have kind of gone to the root of the performance issues using some of the principles that we got from MLXray. Okay, it looks like Michelle's mic is off now. So, I guess resources. The MLXray repo, it's on GitHub. You can just search for it and see kind of what they've been able to do. It's very well targeted for mobile deployments. The MLXray paper, which has been accepted into MLSys. So, if you are kind of part of both worlds, you can check them out at MLSys. And then, finally, you can check out Pixies GitHub repo. It's pixie-io slash pixie. And if you want to check it out on your Edge devices. And that's it. Thank you.


Hey nerds, I'm Jared, and I'm here to review the new Natalie Portman movie Annihilation. Annihilation tells the story of a group of female soldiers who are tasked to go into what's called the Shimmer. Just mysteriously, a risen along the coastline full of all these mutating creatures and weird happenings. Directed by ex-Mackinac's Alex Garland, it stars their aforementioned Portman, Tessa Thompson, Jennifer Jason Lee, Oscar Isaac. Portman is a strong presence as Lena, and she's ably supported by the rest of the cast. Equal parts psychological thriller and horror movie? This is a movie that will get under your skin.  He keeps the tension high throughout, with amazing set pieces and some really gory moments. As the group fractures and their minds betray them, you never know what you're quite looking at and neither do the characters. It upturns expectations at every turn, and it's nothing like I thought it was going in. I also like that there are a couple ways to read this movie.  If I was to pick out any bad parts though, it would probably be the ending. I'm not sure that he sticks the landing on this. As I said, there's multiple ways to read it though, so I could be completely off, depending on your opinion. But it didn't detract from my enjoyment of the movie overall. All in all, it's a cracker of a movie, an annihilation to jump to the top of your watch queue when it hits Netflix on March 12th. What did you guys think? Did you like annihilation? Let us know in the comments below and don't forget to subscribe. And until next time, I'll see you nerds at the movies.


The formal definition of a limit of a sequence has one major drawback. You have to know the limit before you can apply it. This will be an even bigger problem with infinite series. To avoid this, let's consider a few things. So I suppose our sequence has limit l. Then, by the definition for any epsilon greater than 0, there is an n, where for all n greater than n, a n minus l absolute value is strictly less than epsilon. Now, if we take m even larger, then it's also true that a m minus l will be less than epsilon. So the sum will be less than 2 epsilon. And remember, the absolute value of a sum is less than or equal to the sum of the absolute values, but that also works the other way, and so we can condense this and make it smaller. And so we get, and we still have the limit l. So this approach doesn't seem to be useful. So let's ignore it for a moment, but keep in mind the fundamental idea of combining the absolute values. So what else could we do? We might remember that the absolute value of a minus b is the same as the absolute value of b minus a. So that means we can rewrite our second absolute value, combine them, and get. Now it's also useful to remember that if you're off by a constant factor, we can just scale it. So instead of being less than epsilon, we can be less than epsilon halves, and we can adjust the rest of the computations accordingly, and find our differences strictly less than epsilon. And this leads to the Cauchy convergence criterion. The sequence converges if the difference between terms can be smaller than epsilon. Now the proceeding actually proves that if a sequence is convergent, it is Cauchy convergent. We can also prove the converse, but you should do that. So let's prove that this sequence converges. So let epsilon greater than 0 be given. For m and n greater than, well I don't know what, we'll figure that out as we go. We want the difference to be less than epsilon. Now we know what our destination is, so let's fill in the roadmap. And as much as I despise bumper sticker mathematics, here's a useful one. If in doubt, factor out. Here we see both terms are multiplied by a power of one third, and we can factor out a power, although we'd rather not have to deal with negative exponents. So remember, you can assume anything you want as long as you make it explicit. We'll assume that m is the larger of the two numbers. And so we can factor this as and now because this is the absolute value of a difference, we can split it. And because these are sine multiplied by something, we know that these are going to be both less than one. So this is going to be less than. And remember, we want this to be less than epsilon. Well now we have an equation that we can solve and we find. And so we know that n and our lower bound has to be log 2 minus log epsilon divided by log 3. And since we can make the difference smaller than epsilon, this proves the sequence converges. One final note, the algebra here is not particularly difficult, so we often omit the details of the algebra and we replace this explicit computation of our lower bound with a phrase like, for sufficiently large n,


Uh-huh, what's this? A double Christmas Eve upload from Johnny Blocks? Yes it is, boys. Earlier today, we're going to talk about this thing right now, and then later tonight we of course have FNAF AR. And if you don't know what's in store tonight, check out my last video.  This is the first FNAF game to receive a physical copy help wanted. This is exciting, dude. Honestly, this is amazing. I do have stuff to talk about that is not quite so amazing, but just the idea of holding FNAF in my hand is phenomenal, right? It is something that we've been waiting six years for. Maybe just a tad bit strange that it started off with help wanted instead of FNAF 1, but that is simply, sorry, this is going to sound terrible as I open this up, but that is simply because FNAF 1 is bundled in with the core collection releasing on January 15th, I believe. So here it is, help wanted physical in all of its glory. The front cover, really, I have nothing to complain about. The back, however, oh boy, we got some stuff to talk about. So the front cover, as you can see, it's just the, you know, it's just the art of help wanted with all the faces melting together. It's got five minutes and 30's help wanted. It has steel wool down here. It has maximum games, which you may not recognize. That is because they are the publisher of the physical copies. And then, of course, you got teen down there for all those kids that don't believe this franchise is actually for teens. Of course, I picked up the Nintendo Switch, but the PlayStation 4 physical copy is also out right now, mainly because I just don't have a PS4. I will be playing a bit of help wanted on Switch in this video, but I'm just going to livestream the rest on Twitch, which, hey, if you're not following me on Twitch, what are you doing? So the back is where we really got to talk about some things. Steel Wool Studios, whoever put this box or together, we got to talk. Okay, everything else really not that bad, right? Everything down here, I, you know, nothing to complain about.  Steel Wool Lionsgate helped make the game itself. Scott, of course, is the guy behind this entire franchise and then maximum games again is the publisher of the physical copies, but the top bit, right? The top bit is where I have some things to talk about. The screenshots are not bad. It says Classic Frights Reimagined, new horrifying experiences, brand new characters and fun, fun, fun, with all the screenshots of FNAF One, Freddy Potts and Service, Plush Babies and Nightmare Fredbear's Night Terror. But up at the top, right? This banner here that says welcome to your new job. Survive terrifying encounters with your favorite killer animatronics in a collection of new and classic Five Nights at Freddy's trademark experiences where fantasy and fun come to life. So that's not bad. It's just the characters up top. As you can see, some things just aren't checking out. Some things are just not the way they are supposed to be. Hopefully this is folk saying I don't think it is though. But anyways, as you can see right here, Toy Chica, FNAF One Toy Chica, her hands are huge and she's holding the FNAF One cupcake. Why? And then Mangle has both of their eyes, even though they should be missing one of them. It looks like Toy Bunny's arm might be a bit, you know, bent, might be a bit photoshopped, but really that's not as noticeable as some of the others. Yeah, Toy Freddy has no upper teeth. Mangle has blue eyes. Looks like they have a pink tail and it should be white. Just a lot of unfortunate things going on with these characters on the back. So hopefully they can get those all fixed for future releases of the physical copy. But if they do do that, do do. I was like having copies of things that weren't meant to be, you know, like I have the original updated edition of the Freddy Files where it uses like fan made models for the UCN map. I like having that just because they're not being made anymore. So if they change this, I do not mind having this, you know, having poorly, you know, accurate characters on the back. I think, you know, it's pretty cool to have stuff that isn't being made anymore. So on the inside, it's nothing. Yeah, right? It's nothing special. And on the cartridge itself, you know, it's kind of basic. It's just got five minutes and 40 seconds wanted with, who does it have? Maximum games in steel wool, again, with a teen rating, not much. There's no art or anything. It says Nintendo Switch. I'm not really bothered by it. I know some people like, oh, it would have been cool if the characters were on there, like how they are on the cover, but really I don't mind. I think, you know, that's perfectly fine in my opinion. Now, I actually do not own FNAF Help Wanted on Nintendo Switch. So this is going to be my first time playing it on Switch in this video. So let's do that right now. There it is, boys. There it is. Oh, that's awesome. Again, I've never played this on Switch yet. So this is my first time. There they are. Hey, gang. What's up? Okay. Yeah, I have yet to play this on Switch. So I have no clue. Okay. So it's the D-pad. Let's just do a new game. All right. Press B. I don't know why it's B. Usually it's A. That's kind of messing me up. All right. Should be the title sequence. Yeah. Oh, look at this. Welcome to the Freddy Fazbear. This isn't that bad on Switch. Fazbear Entertainment is exchangeable with the digital age. I've seen this many times. I'll just skip this. Can I pick this up? How am I going to pick this up? Oh, God. We do, however. How do I pick that up? I don't know how to pick that up. Why? You acknowledge that Fazbear Entertainment is not responsible for accidental digital consciousness transfer. Re-world manifestation of digital characters, nightmares, night terrors, night sweats. That's a lot. I don't know how to pick up that tape though. So I'm just going to have to go back and do that later on. Ooh. Welcome to the Freddy Fazbear Virtual Experience.  And connect the frightening experiences available. By completing these scenarios. Okay. The world will become available. You'll see plenty of familiar faces and some new ones as well. It's weird to see all the minigames after... ...and have a good time. ...recently, I say recently. ...recently playing the mobile version of this game, where it has like half the content. Fazbear Entertainment not responsible for real danger. Please make a selection from the virtual menu. So, um, again, I'm not going to be here for too long. I just want to play some minigames. We'll start off with Plus Trap. I'll maybe do a few, you know, parts and service, but then I'll call it quits there. I'm going to live stream all of this again on Twitch. Okay, here we go. So, Flashlight is... What is Fla- Okay. It's ZOR. Interesting. Plus Trap. You got a skin coming to FNAF AOR tonight. Are you excited, buddy? I'm going to see this entire room in AOR tonight. Frost Trap. Don't know why they're doing another goddamn ice skin. He looks exactly like Frostbear. They're trying to recreate the magic that they had with a fruity Frostbear. It's not going to happen to Lumix. Just give up. I don't know where he is though. I have a minute left. I do want to see the jumpscare, so if I lose, I won't be that upset. Oh, he's only in the middle. God, hurry up. I have a long time. I can wait. There he is. What's up, man? Again, they don't look that bad. In fact, they look pretty good for a switch. Give him the switch. Okay, give my prize. Oh, it's scrap, not scrap, baby. Plus, baby. Awesome. Next up, some ports and service. I could probably get through all of these, but I'll just do a few. I do want to see Glitchtrap though. So that's on my to-do list of things to do, because I want to see what he's like. Hello, Bonnie. Welcome back to Parts and Service. Oh, no. It looks like Bonnie's guitar. Jesus. Soon it must be recalibrated. Yeah, no, that sounds great. We must access his harmonization line. Get out of here. I need to get inside his secondary throat pipe to access the throat pipe. Both eyes must first be recalibrated. And there's another coin over here. He has to be as precise as possible when removing the eyes from his throat. Yeah, yeah, yeah.  Deposit the left eye and the cleaning receptacle on your left. My thing was over the thing, but the highlight disappeared. God dang it. There we go. Deposit the left eye and the cleaning receptacle on your left eye. Look at that. It's over the thing. What are you doing? Well done. There we go. Now firmly grip the other eye. Is it the right eye? Put it in the other one. Put it in the other one. Put it in the other one. To open Bonnie's faceplate. Now we hit the buttons. Now we hit the buttons. Located on either side of Bonnie's jaw. I'm sure there's some sensitivity options that I could fiddle, fiddle with. Something is right. Blue, green, red. One of those nets is out of tune. It's red. You may push the button. Press the blinking button again to verify your work. I know I'm right.  There's a skip you can do here. Eh. Eh. There we go. Bonnie is in tune and ready for his solo. Boom. Let's close him up. And... Other eye. Then close up the faceplate. There. And close up his faceplate. Well done. That concludes your parts and services task. Um, shadows still look a bit blocky. I remember that being an issue when the game first came out on Switch, so... Hopefully they're gonna work on that but at this point I kinda doubt it. Ooh, a lemon baller. Let's go. Here, I'm gonna go into FNAF 1 just so I can get one tape. Because again, I wanna see what glitch trap looks like. Also, I wanna see what FNAF 1 looks like. Okay, so you got x and y. Can you go into free mode? You can. Okay, good. Nice. So, it's pretty good. Again, this whole game on Switch, really good actually. Pick that up. Get a coin that's down here. Oh god, it's glitched into the drawer. There we go. Another one right here. And so now, hopefully, I should be able to see him. I do want to peek out here and see, how do I... Hello. Yeah, it's very good on Switch. Surprisingly, it works very well. There he is. What's up, dude? Dang, dude, you looking fine. Awesome. So, that's really all I wanted to check out. Again, I'll do more on this over on Twitch at some point soon. Very good. I will say, very, very good on Switch. And I love having a physical copy of FNAF. It's just incredible. I've been waiting years for this. Everyone has been waiting years and it's finally here. So, thanks so much for watching and I'll see you all on the flip side. Goodbye. Gregory, be still. I think she's found us.


Hi friends. Welcome back to my channel and a special welcome if you're new here. My name is Jen. I'm a certified weight loss and nutrition coach and I'm on WW personal points. Welcome to Arizona. Welcome to my new home, my new background, my new office. I am loving, loving not only Arizona but our new home and how my office came together. So let me know down in the comments what you think of my new background. Do you feel like the lighting is good?  Most days of the year here I have lots and lots of natural light in my office. So let me know down in the comments what you think of my new background. Also stay tuned in the future for a home tour. We are still kind of putting things together unpacking, putting pictures on the wall. We had quite a few things we needed to purchase to finish off our home but stay tuned in the future for a home tour. If you are excited for Friday weigh-in it's been a couple of weeks. Give this video a big huge thumbs up. Make sure you're subscribed and your bell notification is turned on because I upload a Friday weigh-in every single week. Check out the description box down below for nutrition coaching. I do offer personalized to you macros and calories. Highly highly highly recommend as well as one-on-one coaching if you would like to chat with me directly. Links, discounts to all of my favorite things and my Facebook group definitely coming over and join us there. That's kind of how you keep up with me more Dave today and it's just a really great supportive community. That is linked in the description box as well. So let's jump into my weigh-in for the last two weeks including traveling from Washington to Arizona, moving, settling in. Let's talk all about my weigh-in. We'll discuss the WW workshop topic, set some goals, and get ourselves ready for a successful next week. I have missed you guys. I have missed filming. I did vlog our trip from Washington to Arizona. I still need to edit that. That will most likely be up this Sunday. So if you want to see our travel vlog, what I ate along the way, how the three-day road trip with three dogs, a U-Haul, pulling a car, my best friend driving another car. It was like the clampets for the three-day trip. If you want to see that vlog, stay tuned for Sunday. So make sure you're subscribed and your bells turned on so you're notified when that video is posted. It was a long three days.  It was a long three days of driving. I will say that our dogs did so well. Better than I could have ever thought our dogs would do. Diesel and Lola rode with me in my car and they were perfect angels. They pretty much slept most of the way. Rachel, my best friend, didn't have a dog with her. She just drove one of our extra cars, loaded with items, and then my husband took Palmer in the U-Haul, and he said Palmer was fantastic. He also just slept most of the way. Lucky for us, all three of our dogs do so well in the car, which is a huge blessing when you're driving for three days and traveling almost 1600 miles. Now, I did pack quite a few snacks for myself, but we did eat all of our meals out. So in that vlog, you'll see what I chose for meals. I got my water in. I pretty much drink water the entire three day road trip, along with just coffee in the morning. And then I stuck with water so that I was able to kind of flush out the fast food or the eating out as well as all the added sodium in those foods by making sure that I'm getting in enough water. We also had to eat out for almost a solid week after we moved into our house because we didn't have groceries and we weren't unpacked to be able to cook in our home. In fact, last night was the first night that I actually made dinner in our new home, which was really, really exciting. I have a beautiful gourmet kitchen. It is one of my favorite things about this house. Definitely stay tuned for the home tour and you'll see it in meal preps and grocery hauls and things like that as well. Speaking of grocery hauls, tomorrow I have a huge grocery haul, massive, massive haul where we had to buy all the groceries we need for the next couple of weeks, as well as my big massive Costco monthly stock up haul. So stay tuned for that. I am finally back to filming videos regularly, so you will get my five videos a week. So overall, everything went really smoothly. I will say, I will say, that I got a rock chip in the windshield of my car, which has now spread and created a crack almost halfway across the windshield of my car. So that is one thing that I have to get taken care of once we get settled into our house. And I'm also having a gentleman come out next Saturday and detailing my car because it's just dirty. And there's dog hair from the travel. Even though we covered everything with blankets and sheets, the dog hair still gets into nooks and crannies and onto the carpet. So I have him coming out this next week, this next Saturday, to do a full detail on my car. And he's a mobile detailer. So he'll just come to my home, which makes it even better. I also have quite a bit of shopping to do at places like T.J. Maxx and Ross home goods. So I'll take you guys along with me for Wednesdays, what I eat in a day. So stay tuned for that for lots of good food, as well as a little shopping, a little shopping haul, lots of good things coming your way in the form of videos. Again, overall, I feel like I did really well with traveling. I mean, yes, I ate out. I just really watched my portions. And I tried to choose the healthiest option or the most well balanced option that I could find while we were traveling. I focused on my water, which I think was huge for not feeling bloated and not having the scale spike because of the fast food and the extra sodium. My goal moving into this next week is to just get back to normal life. Once we get unpacked and settled, which we're there, we're about that far, I would say 90% settled into our new home. We've made several goodwill runs because we had decor that just didn't match with what we were going for here in our old home. We had a lot of rustic and lodge decor, if you remember, in previous vlogs and videos. We decided to veer away from that and go more with the Arizona vibe, kind of like the orange dress that I have on today. Just going more with that Southwest ish Arizona vibe in our decor. So we took a lot of our old stuff to goodwill, and we're purchasing some things that go better with the aesthetic of our new home. We have had people in and out of this house for the last week. I'll share a total update with you guys in Wednesday's, what I eat in a day video. So stay tuned for that. Before we jump into my two week weigh-in, since I didn't have a weigh-in video last Friday, let's talk about this week's WW workshop topic because number one, it's a good one. And number two, this is a question I get all the time as a weight loss and nutrition coach. And that is how to actually achieve the goals that you set. It's one thing to set goals, but it's a whole nother ballgame to actually achieve them. It's no surprise. And in fact, it's human nature that the closer we get to our goals, the more likely we are to actually achieve them. So if the goal that you've set for yourself or the goals that you've set seem like they're going to take forever to achieve, you may want to reevaluate that big picture goal into a little bit smaller goals. Maybe your goal is to do 50 pushups. And that may seem really daunting to you because maybe you're like me and you can barely do 10 pushups. So to set a goal of 50 pushups can be really overwhelming. It's that big number that seems daunting and it feels like it's going to take forever to achieve it. So instead of focusing on that big 50 pushup goal, how about breaking that down into smaller segments so that you can more easily achieve these goals, feel more confident about your overall goal. And remember, as you achieve these small little steps, you're overall achieving that big picture goal. How about starting with five pushups and then once you have five pushups done, up it to 10, 15, 20. And like I said, eventually you'll end up at your big goal of 50 pushups. Once you've done those five pushups, you're feeling pretty good. You're feeling pretty confident in bumping up to 10 pushups and so on and so forth. Well, as we achieve goals, our confidence in that goal boost. And that is really, really important for sticking with long term goals. We can define this as the goal gradient effect. The closer we get to a goal, the harder we'll try to achieve it. And this is just human nature. The closer we get to that big picture goal, the more excited we are and the bigger the push that we have to get there. No matter what your goal is, big picture goal, break it down into smaller steps. This will keep you motivated and you'll actually be able to achieve the goals that you set out. Nothing is more frustrating than never achieving the goal or feeling like it's going to take forever to get to even the smallest big picture goal. Move those goal posts closer and closer so that you'll actually get to the end goal and you'll be motivated to continue to do so. I really like this topic. This is something I really thought about when I started my weight loss journey, knowing that I had well over a hundred pounds to lose. That's a pretty big daunting goal. So for me, it was easier to break that into smaller segments. Weekly goals, monthly goals, even quarterly goals that will help me eventually get to that over a hundred pounds lost. And if you follow my channel, you know that as of my last weigh in two weeks ago, I was down 94 pounds. So that's a great segue into my weigh in. So as of two weeks ago before I started moving, I was 94 pounds down. I didn't weigh in last Friday because my scale was packed and we actually were unloading our U-Haul last Friday as you'll see in my moving vlog on Sunday. So it just wasn't a possibility for me to weigh or film a video. So my weigh in this week is actually for the last two weeks of travel and moving into a new home and I am down 3.4 pounds, 3.4 pounds over the last two weeks while traveling while moving.  And if you stick with it, you can still reach that small goal, which gets you closer to that big goal. So I couldn't be more happy that I'm down 3.4 pounds while moving and while I'm packing and while eating out that entire time. So that puts me at 97.4 pounds. My goal is to hit 100 pounds lost in the month of April. I've been getting a lot of questions. What's your goal weight? How much more do you want to lose? And at this point, I don't have an answer for you. I actually go to see my doctor mid-April for blood work to make sure that my thyroid is functioning better with the medication. And her and I will discuss my weight loss goal and how much more weight that I want to lose at that point. And I'll update you guys in a future weigh-in video. But as of right now, I don't know what my goal weight is and I don't know how much more weight I want to lose. But I will tell you that I do have more weight that I would want to lose above that 100 pounds lost. So now I want to hear from you guys. I want to hear how you've been doing the last couple of weeks. What have been your last two weigh-ins? What goals do you have? Big picture? Small goals? Tell me everything down in the comments. I've really missed you guys and I've missed filming so much. It was a huge priority to get my office put together so that I could get back to filming videos for you guys. So definitely let me know all the things down in the comments. And of course, if you enjoyed this video, give it a thumbs up, subscribe if you're not, and don't forget to ring your bell so you never miss a future video. Check out that description box for nutrition coaching. I am taking new clients. I am scheduling one-on-one sessions and doing macros, especially now that we're settled. I am back to doing my nutrition coaching and don't forget to come on over. Join us on Facebook. We would love to have you. Welcome to Arizona. Happy Friday and I'll see you guys in tomorrow's grocery haul. Bye.


I was familiar with the idea of the Western Maths Writing Project as a history teacher. I feel like I knew they provided professional development. I thought it was more for English teachers. And I knew it was when a colleague of mine in social studies professional development got involved with this project and recommended it to me. I said, oh, I didn't even realize they worked with social studies teachers. That's cool. We teach writing, too. So it seems like an interesting organization. And I like the national component of it and all the different local projects that people do. Yeah, my experience has been great. I've worked with the projects a couple of times before. And it's been really helpful to bring back new ideas and new strategies into the classroom. And just being able to work with colleagues from around Western Maths has been extremely helpful as well. So it's been awesome. This is my first experience with the group. And the networking piece, meeting different people from different schools in different areas and different expertise has been very valuable. Sure. Well, we'll be certified teacher consultants. I would love to. I think it's been a really rewarding experience so far. And I'm looking forward to doing more.


Hey what's good y'all, it's your boy Down for the Down Show of France and we're back to another K-Pop reaction. Now what we're gonna be doing is practice record, BTS, and the panman. I might be getting it wrong, I'm so sorry if I said it wrong, but yeah, we're doing that today. So 2023, BTS faster. So I guess these are basically like the throwbacks that I did. Like you know I think like last year or something like that. Okay, well that's cool. So we're gonna check this out, we're gonna break this down. Like I said before, please make sure you hit the like button, share, ring that bell, subscribe. And also always check and look out my Patreon. I will be having music videos uploaded on there where you go watch a full reaction without no boring, turning the music down and stuff. I got the music up, I'm listening to it, and I'm enjoying the video full out with no cuts. Okay, unless I have a blooper then I gotta cut that. But anyway, let's get into this right now y'all. All right, make sure this is set, make sure I don't know my face. Yeah, okay. All right. All right, let's go in three, two, one. Okay. So was this like an audition? Okay. Hey, hey, hey, hey. Okay, hold on. I ain't got nothing to say about the dancing yet. I just want to ask, was this an audition? It's a throwback, so I just want to know, was this for an audition? That's all I wanted to say. I don't have nothing to say about the dancing just yet. Give it a second. We gotta let him aerate. See what we got going on. Okay. Hey, hey, hey. Okay. Yeah, definitely look like an audition, in my opinion. But if not, I definitely say was getting ready for a concert. Got the mic right here and everything. Definitely get ready for a concert. Definitely get ready for a concert. So I actually want to talk about this part. Not really the choreography, but experience of what happens when time, you know, really works in your favor as you come up in the dance world. Like I bet you a lot of the movements that they probably did in this, like in this moment, was like they had to give everything they got. But BTS now, they'll walk through this. You start to feel more comfortable working together. You feel more comfortable making a choreography. You feel more comfortable and just like really just being in the moment. You feel what I'm saying? So I'm just looking at this and this kind of makes me think about like what I went through to get to where I'm at, and then just seeing them get down like this right now. I'm just watching kind of like, okay, they really, you know what I'm saying? They really grew up. They really, really did. And the shoot game was still cold. Great spotting. Great spotting on this part right here. Great spotting. One and two and three and four. Yeah. Great spotting. Great spotting. Good execution too. At this time, this is real good execution. Good work. Keep going. You know, with that move right there, if you go back and watch this part right here, this, the punch, not here, but right here, based on how you hit that, you got to definitely watch your balance with that because you can, you can keep doing that and mess around a trip if you don't watch what you're doing with that movement. Real talk. Okay. Right there shows you for me personally, shows me the potential that they had.  Because this definitely looks old. You know what I'm saying? Definitely shows a throwback. You know, definitely, you can look at the shoes or you can tell. But honestly, you can see sparks of what they was going to become in this choreography. So that's why I'm giving a real reaction because we've been watching BTS, a lot of BTS, you know what I'm saying? So it's, it's not the same reactions like more like you getting to understand it more like, oh, okay, got it. Got it. This is where y'all at. This is where y'all was at back then. Okay. Now that move right there was cold. Right here. That was, that was, that was cool. That was cool. It's simple, but it was cool. It was cool. I like the flow of that. Now, you know, it was crazy. Here's my review on that part. So that moment of watching this, we had two minutes and 22 seconds, 27 seconds. Sorry. So the BTS now, when they go into the choreography while they're singing and rapping, they have flow right into the transitions. Like, and you can see in this one, like, went back then, like they was always setting up and then going, BTS now. Next phrase, next phrase. You can just see the, the maturity, like, like, wow. Like, if you think about what, what they look like now with the maturity and what they have here, you can see sparks of the potential. Yeah. Yeah. Like I see him working on his mic fixing his mic while he dancing and stuff like that. Yeah. Getting adjusted to it. You feel what I'm saying? Getting adjusted to everything. I still like that transition. Hey, hey, hey, hey, hey, keep it going. Keep it going. Yeah, keep it going. Keep it going. Ah, did he, did he land that? Okay. I see what he did there. That was a smart step. Keep going. And see right here, I can already tell that we, I don't even have to look at the bars at the bottom of the YouTube to see how much we got left, but BTS has always shown this moment where they just, they just go off. And this is where you see, you know, the potential that they are, who they are now right here. And I haven't seen this part, but I already got a feeling. They go go. Boom. Push through, push through. Uh-huh. Uh-huh. Uh-huh. There it is. There it is. There it is. That spark, that spark.  Look how far they came from this and this and this. And you see these moments. It's a Luke hero. Got it. Got it. Okay. Okay. Okay. Okay. Okay. Okay. Okay. Okay. Okay. Yeah. It's cool to go back and look at their old work and just take a time out to just really just watch and just really get like a real review, you know? So, um, if you see, um, you're going Patreon, you'll see the full video of this that if you're watching the full video, that means how they make no cuts, but the one on YouTube probably see I made some cuts because YouTube try to take this down. But no, it's dope. It's really dope to just to get a chance to see like old practice videos and stuff like that and see how far they came. That's really tight. That's really, really tight. So what are your thoughts? What was your favorite throwback for them? All right, but I'm gonna watch more of these. Don't worry. I got more and more on the way. All right. So, um, I didn't, I don't know if it was an audition. I could have been wrong. I apologize, but yeah. Yeah. Thank you. Thank you for letting me know about this video. Yeah. Got more to watch. All right. So I will see y'all soon. Peace.


Will be good. Somebody please pray for God's blessings for God to lead us and then we will start today's discussion. Who would like to lead us in a word of prayer? Manu, you're on the call. I think it's been a while, right? You haven't been able to join recently. Yeah. Hope you're doing okay? Yes ma'am. Okay. Will you be able to lead us in prayer? Yes ma'am. Sure ma'am. Thank you. Go ahead. Thank you Lord Jesus for this day. Thank you Lord Jesus. I submit Lord Jesus this day. Hallelujah in your hand Father God. Father God I pray to you Lord Jesus as we are going to... Lord Jesus learn some more things Lord Jesus to discuss. Father God lead us Lord Jesus. Holy Spirit I welcome you Lord and dwell in us. And Lord Jesus teach us Lord Jesus through madam. Thank you Lord Jesus. I submit all prayer in my hand Lord Jesus. Amen. Amen. Amen. Thank you Lord. Amen. Thank you Lord. Thank you Jesus. Yeah. Thank you Manu. Thank you for leading us in prayer. So we'll get started with today's portion. If you are concerned that we are taking a lot of time to kind of go through some of the sections here in the book of Acts. Don't worry about it. Depending on the content that we cover, sometimes the pace is a little slower, sometimes it's faster. Now I really don't want to rush. I want to make sure we look at as many details as possible. Okay. So that's the reason that in some places we may feel stuck, but you know it's good for us. In Acts chapter 11 so far what we saw is we saw that the believers who got persecuted, they were scattered throughout the region. And they did the work of the ministry and we saw a place called Antioch. There are many Antiochs. At that time there were several Antiochs, you know that cities that were named Antioch by a certain ruler because I think it was his father's name that he wanted. So there are lots of Antiochs, about 15 Antiochs. So whenever we talk about an Antioch, we need to know which Antioch we are referring to. But we are basically referring to Syrian, the Antioch of Syria where the believers had planted a church. And this was a church which was doing well, which the elders in Jerusalem heard about. And the moment they heard about this church, they sent their colleagues, so Barnabas was somebody who was sent to this church because you know a beautiful thing about this church is it was, see again it was planted by believers. It was not planted by some apostle or you know some great. We may think that they have a certain anointing and they are the ones who have planted the church. But of course for the growth of the church, we need the anointing, we need the teaching anointing, we need the prophetic anointing, we need all of that to continue the church. But while the church began, you had just like regular people who started the church. And the beauty of this church in verse 21 it says, the hand of the Lord was with them and a great number believed and turned to the Lord. You know how wonderful, what does a church need the hand of the Lord to be upon it? And there was great multiplication and growth that came about. Hand of the Lord means the strength of the Lord, the blessing of the Lord was on the church. And today what do we seek for our churches? That's what we need, right? We need God's leading, we need God moving upon us. And the hand of the Lord is something that we desire every local church. We desire that and when God's hand is upon our lives, what happens? We see the church of Antioch that it great number believed and turned to the Lord. So it's growth, church growth, we talk about it, right? So one of the key things is that we need God's presence, we need God's blessing and leading. Now just backing up a little bit, before this we had talked about Cornelius. Cornelius who is from a Gentile background and God called Peter to go minister to him. And it was a historic event. How do we know it? In one sense, there is a repetition of what a dream Peter had. He once sees that and then he explains it to Cornelius and then later when he comes to Jerusalem in Acts chapter 11, the other apostles question him. In fact, they are angered. They say, how could you go and how could you eat with the Gentiles? Now eating is a sign of deep fellowship. Now Jews never would do that with Gentiles. But Peter, because of the change of heart that he had by the leading of God, he ended up fellowshiping with the Gentile known as Cornelius. And he shares this with the other apostles in Jerusalem and they are upset with him. And then again by way of repetition. So in scripture we know generally when there is a repetition like a dream is repeated, it is significant. So the explanation is repeated.  I saw a vision in that vision. God showed me the kosher clean, unclean animals and all on the same sheet.  So basically he explains and says, God led me. And at the end of that we saw how God is working in the lives of the apostles. They were silent when they heard this account by Peter. They were receptive of the message that God is now moving into other communities and he's touching the lives of believers. Now, you know, all this teaches us that the Church of Acts was open to the leading of God. They were not stuck in their own biases. They were not stuck. Yes, they revolted when they saw that, you know, Peter was doing something that traditionally nobody would do. But when they understood that God is directing them outside their box, their area, they were happy. They were like, okay, fine, you know, God is touching many other communities. So these are the things that we have seen. Now in the Church of Antioch, which is doing very well, once, see again, the elders in the Church of Jerusalem, they were the kind who knew that equipping the believers is very important. You know, planting churches, sometimes we may take pride in that. Oh, we have five churches, we have six churches, we have 10 churches. Now, the number of churches is wonderful, but the equipping of the saints, the maturing of the saints in the churches is also of importance. Now, in the Church of Jerusalem, whenever the elders heard about a church, you remember when they heard about the ministry of Philip, they immediately sent Peter and John for adding to the revelation which the people in Samaria had. So about the Holy Spirit, you know, the baptism of the Holy Spirit, they did not know. But when the ministers went from Jerusalem, they imparted this revelation as well. Now, the Church of Antioch, is it a good church? Is it a thriving church? Is it a dynamic church? Very much. It's doing very well. So what is the need for the Church of Jerusalem to send somebody to equip them further? But we see that the elders do this. So they sent Barnabas to go to Antioch and when he comes to the Church of Antioch, again, you know, so beautiful, it says, he had seen the grace of God, he was glad and encouraged them all that with purpose of heart, they should continue with the Lord. So again, you know, we are understanding that the Church of Antioch was a good church because even Barnabas was so happy, he was glad. He saw the grace of God upon them, he encouraged them, it says. So that is what we have understood about the Church of Antioch. Now, Barnabas is there and again, it says great many people were added to the church. So overall the church is doing very well. But, you know, we go on to see that at one point Barnabas goes to search for Saul. He goes to Tarsus itself. Remember, he was in the areas of Damascus and Arabia for a little bit and then he went away to Tarsus because people were not ready to accept Saul. They thought he was, you know, like an impostor, he was trying to gain the favor of the people but he was actually against the believers. That was the idea which the believers had. So they didn't believe him. But he went back to Tarsus and, you know, this was like several years had passed by maybe about 12 years or so had passed by in Tarsus and we don't know much about the ministry of Saul there. But we know that, you know, these are the years that God really built him up and he was engaging in ministry. He was growing in the revelation of God's Word over his life. So there was a growth but it was not a time of public ministry in the life of Saul. Now, why does Barnabas go to find Saul to bring him to Antioch? You know, we have already seen that Antioch is a thriving church.  He may have felt that he needs an additional hand. You know, whenever the work of the ministry increases, what happens? We end up needing more people to serve. So maybe that was the reason he would have thought, OK, if Saul comes, he can also help me in teaching and equipping the saints here so that they will mature in the things of the Lord. So that is the reason he goes and it says he seeks Saul, meaning to really search for Saul. And when he found him, he brought him back to Antioch. And then what happens? For an entire year, for an entire year, what is happening? Equipping, OK, training, OK. A great many people were taught, it is said, OK. And at this point, when they were taught so well for an entire year by leaders like Barnabas, leader like Saul, at the end of this, we are hearing that for the first time, the disciples are known as Christians in Antioch. So till now, the term Christian has not been used. But now, you know, in Antioch, the people are being called as Christians. So so far, what were the believers called? Did they have any name? Did the movement have any name? Do you recall? Tell me, I think from your memory, we have discussed this. Brethren, OK, very nice. What else? OK, Christ follower. When we read about Saul, he was persecuting the fill in the blanks. The term was used. Disciple. OK, disciple, yes, disciple we have seen. Church, maybe not. Believer, OK, they believed, it says. You know for the movement, OK, God's followers. All right, so you know what? There were a few terms which were used to describe the believers. Disciples, saints, believers, brothers, witnesses, followers of the, remember the term, the way. W-A-Y, which was used, OK, W-A-Y, way. So Saul was persecuting those who belong to the way you remember. So this was also a term that was used. And yes, now finally in Acts 11, for the first time, the believers are being known as Christians. So Christians means what? Similar to disciple, OK. It basically means somebody who is a Christ follower. A disciple is a follower and a Christian is a Christ follower. So that is the meaning. And here is where you see the term Christian for the very first time. And the Church of Antioch is equipping its believers. Now let's continue to see what happens in the Church of Antioch. So now we are at verse 27, OK. So in the time when the Antioch Church was growing, there came some prophets also from the Church of Jerusalem. We all know that God has given the five-fold ministry offices for the equipping of the saints. So you see how beautifully the Church of Jerusalem was interested in serving local churches which they heard of. So when they heard the Church of Antioch was doing well, they sent a leader and that leader took on the responsibility to equip them with teaching. OK, so Barnabas saw for one year they taught. What could they have taught? They could have taught them. Earlier remember we said the Apostles' doctrine was taught to the people. We said that the teachings of the Kingdom of God and about the life of Jesus, these are all the teachings that we can expect Paul and Barnabas to have imparted to the believers. Now the prophetic is required. So all these things will cause the growth of the Church. It will cause the growth and the maturity of the believer. So now prophets are coming from the Church of Jerusalem to Antioch. One of them, that person's name is Agabus. And what does Agabus do? He stands up and he prophesies that there is going to be a great famine throughout all the world which happened in the days of Claudius Caesar. Then the disciples, each according to his ability, determined to send relief to the brethren dwelling in Judea. This they also did and sent it to the elders by the hands of Barnabas. So this is a feature of the Antioch Church. It's a church which was already doing well. A lot of people are being added to it. Then the church was equipped. Now prophets have come to the church. And what else do we see when they hear this word? They believe in prophecy. Apparently Agabus is a notable prophet during those times. We will see Agabus's name once again in the book of Acts. Agabus gives a prophecy about a famine. And you see that the Church of Antioch responds. Nowadays if we hear, suppose let's say there is a prophecy that there is going to be a difficult time and churches are going to struggle and we come to know about it. What should be our response? What do you think? Somebody comes to us, a notable prophet. We can trust the word which he is saying and he is saying there is going to be a famine in this country. What will be your response? You can unmute an answer. I mean you don't even have to type in the chat. If you hear that there is going to be a famine, what would you do? Okay, come on believers. How will you respond? Pray about it and seek for confirmation maybe. Yes, true. And prepare for the decision. Yeah, very good. Very practical also, spiritual. They were saying we will pray and he is also saying we will prepare. What should be done? Very good, very nice answer. Anyone else, how do you think we should respond? How would you respond? Do we plan to respond? We are all just thinking what would be the best way. Manu says she will arrange things. Okay, very nice. Engaging in some sort of a practical way of helping. That is how Manu would respond. We have seen so far some spiritual way of ministering which of course we can pray, we can prepare. Practically Manu is saying we will try to give help. Now if you look at the Church of Antioch, this was before them. They know that there is going to be a famine. How are the people responding? You see the early church, earlier remember there were people living in Jerusalem who did not have resources. What did the church do? Okay, so the Christians we see them really being a powerful witness. Not just in the spiritual matters. It is a praying church, it is a worshipping church. It is a church which is sitting to listen to the word of God. But when it comes to issues of practical concern, it is also a church that is responding. So the Church of Antioch, everyone according to his own ability. Again, there is no compulsion. The church was not forced. You remember even Ananas and Safara, there was no compulsion that they had to sell and they had to give all their property to the church. There was no compulsion but they lied. They tried to make it look like that. But everyone according to his own ability is what even God expects. The people, they collected. Like Manu said, made some arrangements, whatever they had, they put it together so that they could send it to help the brethren or others who believed in the region of Judea. So such a beautiful, you would love to be part of such a church where you are being taught the word of God and people are also practically responding to the challenges around them. So that is the kind of church the Church of Antioch was and it's a blessing to really know about such a church. So what did they do? They determined it says to send relief. Wow! That means the word is really working in their hearts. They are not just trying to be spiritual but they are also practical. So they determined to send relief to the brethren dwelling in Judea. How did they do this? Again, a lot of wisdom. How did they send the money? A good way to do it is they sent it to the elders by the hands of Barnabas and Saul. So the trusted people in the group were obviously the leaders, Barnabas and Saul. So they got whatever they wanted to give and they sent to the hands of their leaders to Jerusalem. And Jerusalem, there the leaders could decide which region, which are the most needy churches. Come on, let's send this money to them and let it be a blessing to the people. So this is what is happening that we have read a little bit about the Church of Antioch. Now let's move on and see what else is happening around the same time. You had the rule of Herod. Now this Herod is Agrippa I. He is the grandson of Herod the Great. So Herod the Great was the one who ruled at the time when Jesus was born. It's not the same Herod that we are talking about now. This one is the grandson.  We do understand that the period is one of persecution and there is persecution coming from so many sides. We've already seen how Saul was treating the Church. We've already seen how Stephen was martyred. Now at the high level, at the authority level also you observe that King Herod he is going against the believers. Now we can also use the term Christians to describe the believers. What did he do? So far it seemed as if only the congregation was bearing the brunt of the persecution as if only the people who were being taught are the ones who were the target. But in Acts chapter 12, we see the martyrdom of an apostle. So we read in verse 2 that he killed Herod James the brother of John with the sword. Which tells us generally the term with the sword means that he would have been beheaded. So one of the apostles James the brother of John. There are two James. Don't get confused. One James is the brother of Jesus. But this James is the brother of John. So the brother of John James was beheaded and we can understand that even the apostles were on the hit list of the authorities and they were waiting to persecute both the apostles as well as other believers who were following Jesus Christ. So very unfortunate and it must have been a time of shaking for the church because so much of opposition and direct opposition against them. Now what happens? And when Herod saw that what he had done actually made the people, the Jews very happy. He went ahead and it says that he caught Peter and he caught him, put him in the prison. Now why did Herod do this? Different persecutors as we study from the time of Peter and John walking into the temple and them healing the lame person. What were the leaders afraid of at that time? They were afraid that the people will turn their trust and put their trust on these apostles and their trust will be moved away from the existing leadership. So that was the fear. Later when you look at somebody like Saul persecuting you observe that he was zealous for the work of God but he was zealous for the wrong things. So he had a reason why he was persecuting. Now looking at King Herod, why is King Herod persecuting? The reason is purely political. So you notice here that he went ahead and he killed James the brother of John and he got a good response from the Jews. The Jews would have been very pleased with the king. Wow what a brave king, look at him. He's stopping these so-called followers of Jesus and Christians. So he wants to get additional praise and acclaim from the Jews. So he decides okay let's make this better. How about you catch another apostle? So does Herod have a sort of a better reason to persecute the believers? Doesn't look like, it just looks like he wanted to please the Jews and hold on to his position and his authority. So that is why he goes and he seizes, it says Peter, puts him in the prison. So Peter is now arrested. Okay, but what happens is that time it is a season of unliving, the days of unliving bread. So they are following certain Jewish rituals at that time and because of the period where this arrest takes place he's not able to execute Peter immediately. So what he does is he puts Peter in the prison and he puts four squads of soldiers to keep him. Now four squads of soldiers, usually they would not put so many soldiers to take care of a prisoner. But as if the apostles were so dangerous, they're trying to prove that these people are very, very dangerous. So there are four squads of soldiers to guard Peter and they hered again to please the Jews.  So that is Herod's plan and Herod is only after pleasing the people. Now what is the situation on Peter's side? Peter is in the prison, we are told. Now in such a serious situation, one of your leaders just got killed and one of your leaders is now in prison, what would be the response of the church? Suppose something like this happens today in our church, what would we do? Come on, think with me, class, how will we respond? It's scary, isn't it? Yeah, so what would you do if one of your leaders is in the prison and you know? Yeah, so what have we seen the early church do generally when they get into trouble, what do they do? They gather and they pray, what do they do about it? Yes, exactly, exactly. So amazing response, isn't it? We would think that we will try to find the person who is highly influential among us. Okay, let's see if we can contact the authorities, bring our leader out. Those are all certain practical things that run through our minds, nothing wrong with it. But the response of the early church, they depended on the Lord, they prayed together, that was very, very common, their practice. So we notice once again over here that they are coming together. It says, but constant prayer. And that word constant there, it is from a Greek word called ectinos which is comparable. In fact, it was the same word which was used for Jesus agonizing in the Garden of Gethsemane. Luke 22 verse 44. So it tells us constant prayer. What kind of prayer did they pray? It was not a prayer where the apostles put a timetable and said, huh, time to pray. We are in this situation, we are announcing 40 days of fasting and prayer, you people pray. So then people come, yeah, okay, we have to pray. It was not like that. But constant prayer means from the heart, the sense of feeling. And it's not just emotional. I don't know how to explain it, but earnestness, sincerity, from the depth of their heart, just the way Jesus prayed in Gethsemane. Was he serious in his prayer in Gethsemane? Yeah, he was travelling. We studied about that, you know, the prayer of travelling. So he agonized. He felt it in his soul, in his spirit. He kind of feels it and he reaches out to God in the same way the situation that the church is in, they are going before God and see that they are offering constant prayer. Okay, Peter is in the prison. We just lost a leader, God, we don't want to lose another leader. Okay, and they are praying for Peter. Wow, what an example. You know, we see that they are called as witnesses. Jesus said, you will be my witnesses, right? What a witness for us today to follow their example. They were sincere in their prayer to God and they were praying for Peter.  The church has to continue to thrive. So these are all the prayers they could have been praying, but they were sincere and they offered constant prayer to God.  So he decides, okay, tomorrow soldiers bring Peter out. So what is happening?  You just imagine, okay, somebody is in the prison. Suppose you are Peter, I am Peter, in the prison. Is it even possible to sleep tomorrow? You know, I might get executed. That might make an individual so anxious. You're wondering, you're thinking, oh my goodness, what do I have to say sorry to anybody? Do I have to pay anybody? You're thinking all those things because tomorrow can be the execution. Just now James died. But what is Peter doing? What is Peter doing? Yeah, correct Manu. Sleeping, how can you sleep? You know, it's incredible. It's my interpretation that till now Peter had developed that confidence. Remember, even earlier they caught him. They took him for interrogation. So many things happened. The angel came and opened the kind of rescued Peter at that time. So Peter must have been hopeful that no problem, let them do whatever they want. God knows how to rescue me. Why should I spoil my night sleep? Let me enjoy my sleep. So he's actually sleeping. Or who knows, maybe he was exhausted. That also is a possibility. That is why he's sleeping. And we're told that he was bound with chains between two soldiers. So is there a way of escape? Not at all. How can he escape? No way. And guards before the door were keeping the prison. So high security zone. Now what happens when people pray? Here is the result. Now behold, an angel of the Lord stood by him. So when the church is praying, God is sending a supernatural rescue. Supernatural deliverance. An angel stands before him. And how does an angel look? Light's shown in the prison. It's standing before him. And he struck Peter on the side and raised him up saying, Arise quickly. And the chains fell off his hands. So the angel is delivering Peter from the chains. Then the angel says to him, guard yourself and tie on your sandals. Or kind of get ready because you need to go out. And then Peter follows that. He puts on his garments and he follows. Now the angel is leading him. Where is the angel leading him? The angel leads him past the first and the second guard post. Then they came to the iron gate that leads to the city which opened to them of its own accord.  Chains come off. And Peter is wondering, is this real? Am I sleeping? Is this a vision? Is this even a state of confusion? Because he's in that sleep mode. But the chains broke. God is showing him how to get out of the prison. And he's coming to the iron gate. And what do you read? The iron gate. It says automatically. It's like a movie. It's unbelievable. It says which opened to them on its own accord. How can an iron gate open on its own accord? Tell me. I don't know. Nobody knows. But when people are praying these miracles are taking place. Supernatural deliverance is taking place in the life of a leader. The iron gate is opened. Then what else? And they went out and went down one street and immediately angel departed from him. So what did the angel do? Guidance. Okay, come. Peter, you don't know where to go. It's dark. You're sleepy. You might stumble and fall. Follow me. So go this way. That way. One more street. Went down one street. So correct road. Where should Peter go? That also he doesn't know. But the angel leads him. And he comes out and Peter finally when the angel left and he realizes this is not a vision. This is real. You know, you kind of pinch yourself. You tap yourself and you see what is happening. So he becomes alert and it says when Peter had come to himself or he realized this is not a vision I have really escaped from the prison by the help of an angel. So he understood. Now he says, now I know I'm certain that the Lord has sent his angel and has delivered me from the hand of Herod and from all the expectation of the Jewish people. Isn't that amazing? Is God able to rescue his people from the prison? I think this is like, you know, Peter's kind of second experience. He has been rescued from the prison and he knows that, you know, he's our God. He can deliver us. If he wants to deliver us, God can deliver us. Now, some people may ask the question, why is it that James was killed by the sword? But we have Peter here. Who has escaped the sword? God, what is the logic behind this? You know, it's hard for us to answer a question like that. But only God is aware of the lives of the people. Now, James, do you think God was upset with him because he got martyred? No. We know how God treats the martyrs. In the life of Stephen, we've seen it.  Now, why is it that some people are martyred? It's hard to answer that question. But we know God's response. You know, God receives the martyr in such an honourable way. So, was James any lesser than Peter before God's eyes? No. Why did Peter escape? Why did James die? I don't know the answer to that question. But God's honour over the life of James, that is understandable. He became a martyr and we know how God treats martyrs, how Jesus treats martyrs. Jesus told Saul, Saul, why are you persecuting me? Isn't it? And now Peter, Peter has escaped. Maybe, we can look at it this way. Maybe there was something more for Peter to complete through his lifetime which is why it was not yet time for him to go to God. So, he continued to live on. Peter continued to live on. He had a supernatural escape through the guidance of an angel. And this happened because the church was praying for Peter. So now, when we see, where did the angel bring him? The angel actually brought him to a house. In the house of Mary. Mary was the mother of a young man called as John Mark. And in the house of John Mark, the believers were gathered together in prayer. And because he's at this door, Peter understands. Angel brought me here. Let me knock the door. So, he knocks the door. And a girl comes running out. Her name is Rhoda. She recognises Peter's voice. And she is so happy that she does not even open the gate for him. But she runs and she tells everyone that Peter is at the gate. But the funny part is, when she tells the people this, they say, how can it be Peter? It must be his angel. Because in those days, they had a concept something like guardian angel where a person's angel is with that person and may look like that person. So, they believed in all those kind of things. So, the believers thought it can't be Peter. He's in the prison. How can he be at the door? But don't you think it's a little funny because they are praying for God to deliver Peter. And God has answered their prayer. But the answer is so miraculous that they are not able to accept it. You know, it's like this. I've heard this story where some people, they prayed for it to rain. A little girl goes up to them and says, okay, I brought some umbrellas for all of you. And they say, why are you bringing an umbrella? She says, no, you just prayed for rain. Then you should believe that it's going to rain. But the people say, no, we don't want umbrella. And she's the only one who's holding an umbrella because she's really expecting God to cause it to rain. So, this girl, Rhoda she sees Peter and she's so excited that out of the excitement, you know, she's not opening the door. God has answered the prayer and this little girl is going and telling everybody. Peter just at the door but the so-called mature believers, they say, can't be Peter. We prayed for rain but it's not going to rain. It's like that. But I guess sometimes we have that attitude, isn't it? We it's hard for us to accept that God will answer the prayer. So, anyway that's what happened. Now Peter continued knocking the door and when they opened the door and saw him, it says they were astonished. Wow, it is a miracle. Four squads of soldiers Herod had put how did this man escape? Supernatural. So, they were astonished. But quietly they knew that if they are going to get excited and scream and all in the night, everyone will come to know. So, they quietly tell him, okay, you come inside, okay? And then Peter tells them, you know, God did this. He sent an angel. The chains came off. The angel showed me the way and finally I'm here. And he tells them, go tell these things to James and to the brethren and he departed and went to another place. So, he tells these believers to go ahead and tell which James now, this is the brother of Jesus. Who is the considered as, you know, one of the first pastors of the church of Jerusalem. So, James is the leader. This is the brother of Jesus. So, this is what we have seen so far. What we'll do is, we'll take a small break. We will come back. We will maybe have some discussion. Okay. And then we will continue. I hope you are getting something out of this, everyone. Yes, ma'am. Okay. Excellent. Excellent. Alright. Let's go for a break class. We'll be back at 10 o'clock. We'll continue. Yeah. Wonderful. Thank you. Thank you everybody. God bless.


Hello everyone, this is financial author Amit Don of Aeron Journal. Today I'll talk about cashback credit cards. I prefer travel rewards credit cards because they provide maximum returns for your dollars. However for ease and simplicity some of you may want to go with cashback rewards credit cards. Today I'll go through briefly some cashback rewards credit cards that you can consider so you can pick the one that suits your needs. MB&A Rewards World Elite Mastercard Although marketed as a travel rewards credit card, the MB&A Rewards World Elite Mastercard provides 2% cashback across the board with no strings, no limits, no caps, no tears, no problems. Anulfi is $89. Scotia Momentum Visa Infinite Credit Card With 4% cashback on groceries and gas, 2% cashback on recurring bills, and 1% on everything else, a perfect cashback credit card for those who want maximum return on selected categories. Anulfi is $99. BMO World Elite Cashback Mastercard A flat 1.75% cashback across the board without any limits, provides the best insurance benefits among all cashback credit cards. Tangerine Moneyback Credit Card Options to choose up to 3 categories where you can earn 2% unlimited cashback, Anulfi is free. The Simply Cash Card from American Express A flat 1.25% cashback on everything without limits, Anulfi is free. There are many other cashback credit cards available on the market, however I believe these I just mentioned offer most value for your dollars spent. Do your research before picking any credit cards and stay with the one that most suits your needs. That's all for today, thank you.