Okay, hello everyone and welcome So yeah, as you said, I'm gonna talk about the new Firefox profiler today, and I'm now some John I am a software engineer at Mozilla, and I'm working on the performance tool in team You can find me there So the Firefox profiler is essentially the profiler that firefox.com So you can visit there and there are some instructions, but I'm gonna walk you through everything. So bear with me So this is a typical like screenshot from a Firefox profiler and like What's happening here? Like there are a lot of stuff going on like there are a lot of colors. There are a lot of graphs so It's kind of intimidating at first for peoples to use that tool, but I'm gonna walk you through all the panels and every detail So you're gonna be more comfortable to use that tool once we're done So but essentially we should take a look at back and like we should learn what is a profiler first so profiler essentially helps developer to analyze the performance issues and Gives insight or into how Program works, so it does that by sampling the pro program. So what is sampling then? so Profiler stop the execution of the program in a like a fixed rate for example one millisecond so And records the relevant data for example that can be a current stack It records the data and resumes the profile program later so in this graph you can see a simple program and the work the vertical lines are the profiling profiler sampling and those straight lines are the program execution and Main calls a calls B and call C So as you can see on the first peak first sequel actually a Profiler missed it because like the red arrows are the stack of the current Program and we managed to capture the main B, but at the first peak we actually managed to miss it because like the C runs less than one millisecond and It just falls between two sampling time and We didn't see it but rest of it like as you can see on the second peak second sequel we actually managed to capture that call so it gets all the stack information in an interval time and Once we have that we aggregate those data and we create something like this a call tree So this is an example from Firefox actually So there's a main function and they're from the main there are other calls So we sample Every millisecond and aggregate that data and also we create those timings from that that aggregated data I'm gonna talk about the time the timing later So yeah as we learn the samples provide a view into the profile program But as you can see on the first sequel we can miss some stuff that happens quickly So markers to the rescue as an additional to the sample data in the profiler we also have marker data and What are markers? So they are also very similar to samples. They are they provide a view into the executing code But they don't miss anything because we manually add those information in the source code and We also include additional information for example in this picture There is the call stack the stack and then there are some Additional information for styling so this is a marker that we add whenever there's a new Styling happens in a web page So we learned those two Main data sources from a profiler, but what is the Firefox profiler now then? So the motto of the Firefox profiler is capture performance profile Analyze it share it and the make the web faster so this is again the same one but there are two main advantages of Firefox profiler and The first one is you can see both JavaScript and the native call stack in a single call tree What that means is so when you run a JavaScript? function in your web page and if that function for example as a DOM element and we need to see the DOM edition in the Firefox source code so We also after that JavaScript Frame we also see some Firefox related native code execution so you can also see that those informations as well Also, you can filter to just JavaScript only so if you are profiling your web page you can just see JavaScript that that's what it's important to you and The second part has two branches The first one is for actually non-technical people So if you're a non-technical person you can just capture a profile for example Firefox is a performance issue and You you have you can reproduce that but You don't know what to do So what you can do is capture a profile and then share it with an expert in this case you can create a bug in bugzilla and you can share the URL of that specific profile data and Some expert can come and see that profile later Also, if you're a technical person you can capture it yourself it can be again a web page or Firefox and You can save it into your desktop or you can share it and keep the URL and then take a look at your data later So we'll now learn that there are actually two main UIs in this first You need to be able to capture a profile And then you need to be able to analyze it. So we're going to see the first capturing ui and How to capture a good profile data so first you need to go into the profiler.Firefox.com and You just need to follow the instructions. It's pretty straightforward. There is a big Button that says install add-on. So you need to install the add-on first and once you install that You're gonna see this pop-up So this an icon will appear on the top right side of your Firefox and once you click that this pop-up appears and There are two big like main buttons here. So once the first one is for you to Start recording or stop recording and the second button is to capture that profile So a work for a typical workflow is this first you need to Make sure that you don't have any background task or tabs in your Firefox So you need to isolate that performance problem as much as possible and once you do that you need to start the profiler and After that you can do the work that that do you think there's a performance issue for example you can if there is a Performance issue during the page reload you can start the profiler and then reload it wait until it it's done And then capture the profiler Once you do that a new tab will pop up and It's gonna bring you the profile at Firefox.com again And now you're gonna see the data there and you're gonna see the analysis data Analysis UI that we've seen before Okay, so now we captured the profile data and now we can actually Analysis and try to analyze it So this is the UI. I know it's complicated at first, but this section is the timeline So as you can see on the top side here, there are some timing information and here at first Row there is a screenshot Track so it also records screenshots of your Firefox. So you can actually see the UI and the code at the same time and try to see what is happening here and You can also hover over those and try to see the bigger screenshots and In this section in this process This is the stack graph. So we were capturing this stack During the sampling now we have that data and we aggregate that and we show a dense view here So it's not great accessibility wise because there are a lot of colors. We're trying to make it better But the important color for example here is the yellow one because that means JavaScript category So you can also see other ones for example Dom as blue and etc and Here you can see The markers that we mentioned before they're more precise. There are a lot of them so we again put it into add dense through you and You can hover over those and see the date details of those markers For example, this is a styling marker and you can see some relevant information About that marker and you can see that took 17 milliseconds, which is quite long usually and You can also actually Select a range during that timeline and then you can click into that Magnifier icon in the center and you can actually make it make that view the full view and then you can zoom into that and as long as you want to See what's happening there and the other thing is we have the panels So at the top of the profiler We have the dense view that we put everything but on the bottom side there are more Information for you to see This is more detailed. So I'm not going to go into each tab right now because we're gonna see Those into the demo slide. So That's easier that way But also so now we are familiar with the UI But if you're a non-technical person, you don't have to care about that you can you should just know how to share that profile so Inside the profiler data. We have a lot of Different kind of data the first two ones are that we mentioned Those are the main ones samples and markers and we have screenshots network requests Metadata etc. So keep in mind those and so Once you get the UI actually there is a button on the top right corner named publish so you can click into that and this pop-up will come up and Here you can actually remove some of your personal data before sharing it because as we can see on the previous slide there are a lot of information and those information can Include some personal data as well. So here for example, we can Remove the screenshots that can be personal information or we can remove the source resource URLs So once you remove those you can click publish and It's gonna just bring you the URL after that upload session is done and Now you have the URL you can just copy that and send it to someone else or you can post this into the bugzilla comment and some other people can Take a look at that information later and Also, we have single tab and advanced view so this profile UI is Complicated and there are a lot of Firefox related information in it as well But if you're a web developer, you don't have to take you don't have to know those and you can just see Your web content track and you can try to analyze it. And so this is still a work in progress So we are trying to make it the profiler better for web developers. So you can easily start using it, but It's it will happen very soon So you can actually just see the information that you want to see so let's go back to the demo section now and Now we can See those panels and you can see what is happening there As you can see when once you open up that Profile so by the way, you can get those slides here in that URL and You can get that demo Profile so you can take a look at that So here you can click on that and once you have that you can see it So here this is an example profile that we captured before but before that I want to actually Show how we capture it. So we've seen the UI before but still I want to show you how to do that So here not here here. We have the add-on so you can Press start and now we are capturing the information of Firefox and that web page And now you can do some stuff. For example, we are doing the tap switch now to Analyze the performance issue of that tap switch and now we are done with it and we can click capture but I will recommend you to use the shortcuts instead because once you open this Pop-up it actually affects the performance of Firefox like you can it creates a new view and paints it so To you can minimize the usage of that pop-up and then just use the shortcuts instead So that's much better. So once you've done that it captures it. So this is the capturing part and Let's go back to our profile. So we have the screenshots here so you can actually hover over those and see the bigger version of those and for example, this is a profile that we captured during the Wikipedia and We try to open the DevTools panel and then close it afterwards So this part is the one that we open the panel as you can see here. So we are opening this DevTools panel here and this Big stack is the DevTools initialization. So here we start to initialize that DevTools as you can see and Here it's done at the end of that stack. We initialized it and afterwards Here we are closing back again and this stack corresponds to the closing part so you can see what Functions that we are calling during the initialization during the DevTools opening and during the closing and For example here a garbage collection happens once we are done with that data so and Those are the markers that you can just hover over those and see more information about them and usually Red bar means that you need to fix something. There's something Interesting going on there because there's a delay happening there. So you need to minimize the event processing delays essentially and here we are doing a lot of work so we can just zoom into that view as well to see what's happening and Also, we can click into a marker to Automatically select that range and we can zoom into that wheel. So Once you are in there, you can go back here to the full range So let's take a look at that section because there are a lot of Information there and there are some interesting things going on. So we zoomed in here and We are going to See the bottom of the page the tabs so The this part is the part that we need to analyze and we need to see what is happening so you can click each or you can option click and you can Expand everything and you can try to analyze this data. So For example here, there's a start there's a main function of Firefox and there's other functions happening But if you're not a Firefox developer, you don't need to know those you can just Switch here to JavaScript and you can only see the frames that you actually Can change and here you can again Expand those and try to see for example on the left side. There's a running time and this Callback this promise callback takes the 49% of the time and it is 295 millisecond. So it's Very high and we can see the self time here. So the running time is the whole time including the nested function calls and the self time means the Time actually that function itself takes So we can try to see for example. There's a 10 millisecond self time self time happening here. So That's a red flag. So we can try to see what that load function actually does and maybe we can try to Make it more performant or Let's see other things So there's a seven millisecond again the load function interesting so That means that that load function does a lot of work I don't know if it actually has to do it or maybe you can do some tweaks and make it more performant Here another load function, so we start to see a pattern here. So there are a lot of Individual load function calls happening. Maybe we can just merge them together try to call everything at once instead of just doing everything or Yeah, we can just try to See how we can reduce that time and this is the call tree basically. So this is the that and the second tab is a bit more visual. So this is the flame graph and This is essentially the same data with the call tree, but you you now have a bottom up call stack here, so you see the Longest running functions here, for example, this is the promise call stack that we've seen before and Once you go up you see the other functions and You can hover over those again and see More details about those functions and for example, you can see how long overall takes or how long JavaScript interpreter actually takes that time and You can again change this text. You can change the JavaScript only or native only so native only means that Basically C++ rust or if you're an Android it can be Kotlin or Java It depends and this is the JavaScript and if you change it back to all all stacks, it will show you everything here So the stack chart is also pretty similar with the first one But the difference with the flame graph is the first thing. This is the top down and the most important Difference is this X axis is actually the time. So if you Go back to the full range you actually see those frames here and You see those frames here. So you can see the time and information and what frame is being called in what time so and You can go back to marker chart So this is the same data with the those markers, but it's more detailed and grouped for example, you can see the DOM group the garbage collection graphics JavaScript, etc and You can see more information if you hover over those and Marker table is the same data, but with a table Also, by the way, you can filter whatever you want. For example, if you want to see the load Events you can write load events and you'll see load DOM events. For example This is the before load before on load and load and stuff and you can see this network load function markers so And you can do that filtering pretty much everywhere You can do that here as well. You can see only load functions and The last tab is the network tab. So that Helps you to see what network requests are being made in this profile session and you can again hover over those and you can see how long does it take and You can see a more detailed view into that HTTP request Yeah, I think we are pretty much out of time like we have two seconds two minutes. I guess so I'm gonna close up the demo and So you can learn more information in this documentation you can go in there and try to see you can also get those slides and You can take a look at those again And if you have any question, please Just join into our matrix channel. It is profiler and Just ask us anything. We are happy to help you You can just ask us. So thank you. Thank you so much If you have any questions, please ask yeah, we can have like one or two questions Do I ask the next speaker to come and set up? Yeah, I'm coming


Twinkle, twinkle, little star, how are what you are? One of the things that I know for sure is that children learn compassion when they're young. We all learn compassion best when we learn it when we're youngest. It is never too late. But for a program like Roots of Empathy to be able to go into schools and show children what it is to look after someone more vulnerable than you is probably one of the most important things that government can support because it is truly an investment in good citizens and in our country.  I was just so impressed with Miss Ismael's grade 1-3 class at Taipei Elementary. We're so excited to meet the baby and so eager to make observations and share their own stories and ask questions. On behalf of all the moms and dads and babies here today, I just wanted to say thank you so much to all of the classroom teachers who led us into your classes, to all the Roots of Empathy instructors, to the province for funding this amazing program and especially to Mary Gordon for creating it and making it possible for us to be in this room full of absolutely gorgeous babies today. Thank you very much. As the Premier said, when we are trying to raise levels of empathy and compassion in children, it's not just for their friends, it's not just for their family because children are 100% of the future. So when we talk about changing the world child by child, it is through the loving attachment relationship of the parent and the baby that we are learning and the ethic of care is out there on the green blanket and it will be in the classrooms today and in the province tomorrow and in the broader world in a decade. So thank you to everybody for their peace and especially thank you to the parents.


Welcome back, folks. We have the Dow Industries up 14, Nasik down 13, S&Ps down five. Let's go over to our man, Mr. Dave Mazza, who is the managing director, head of product at Direction Shares and of course Direction Shares, folks. We're talking about funds. You're talking about Levin products. In that particular case right here, we're talking banks. We're talking gold. We're talking small caps. Dave Mazza, welcome back to TFNN. Hey, thanks for having me back, Tom. Absolutely.  Indeed.  You know, when we take a look at, well, even the FAS, the FAZ, right, which is in this particular case, the FAZ folks, they're three times, you know, the Levin product of the financials.  What do you guys see on your side when this happens? Yeah, it's really interesting. I think we've seen a bit of a coiled spring when it comes to financials, as many bull strategists from a long-term point of view and traders have been waiting for, you know, the opportunity to pounce. And it's been interesting is, you know, we've been in a market that has been extremely defensive. People have avoided the cyclicals. They've avoided the more value names. And if there's one sector that's both cyclical and value, it's financials. And so when we have these risk on days in the market, you know, we certainly see significant activity on people trying to play that, especially on the bull side, because in FAS, because we've certainly had seen more activity in an area like FAS as, you know, financials haven't had the easiest run, really, you know, sensical financial crisis, but even more recently as rates, and especially the yield curve, continue to be depressed over the summer. Yes. You know, it's amazing that they haven't had a more extraordinary run actually, because they seem to always make money. Like if we look back from here, even before the crisis, they're making much more money now than they were then. But for some reason, you know, the market hasn't jumped on it. They're jumping on it now, but for some reason, there's legs that are involved there, I guess. Well, you know, there's been a, there was a persistent overhang of regulation, right? You know, financials certainly may be benefited and overlaid from a revenue and earnings perspective because of loose regulation. Concerns about whether it's Basel III coming out of Europe or Dodd-Frank here, it's difficult for people to get a sense of clarity on what the picture is going to be from earnings, you know, do they become just regulated utilities in the worst case scenario. Heading into the election, which is actually, we're already beginning to see our trading clients begin to make some interesting bets in that particular space. That's another concern, right? We know, you know, whatever your political opinion is, President Trump and his administration has certainly been more favorable to financials than many people expected. You know, I don't know if the same can be said with some of the Democratic candidates while still early there. So there is this kind of, I think still a little bit of mist of exactly how investors should be positioning with financials. But for traders who can look at both the bull and the bear side, a lot of opportunity is going to be there, especially if we begin to see a continued move up in rates, you know, by market close today. But some of those moves to your point in the last week were extraordinary. And if that continues, you know, we could see a 10-year jump pretty quickly to 3%. I think that gets the market into some other kind of trouble. But that certainly would help the case for financials. Yeah. So, hey, let's go on that side. Because that's, you know, this, the, where the level line is, folks, is so hard in this market. Because just as Dave said, right, is that, you know, the bonds came down, banks are going up, but if the bonds go up too fast, then the market's going to start saying, okay, what's going on? So what I'd love to talk about is the small caps, you know, because it seems that when we take a look at the small caps, you know, those topped out July of 2018, you know, now if we're talking the TZA, the TNA, you know, like what do you think's happening to the small caps? It's amazing that we're at all-time highs and these guys still can't, you know, basically get the juice going. Small caps can't get your break, you know, to your point. You know, they topped out well before the large cap space continued to live, continued to be middling around, looking for support and really have struggled. This most recent earning season has not been pretty for small caps. You know, large caps have seen the beats as they normally do. So I think we're going to avoid negative EPS in the third quarter, but man, small caps so far have not been nearly as positive there. And for the trading community and the long-term community, small caps, while the valuation with large caps, you know, if I look at price to book or price to earnings, price to sales look terrific. If you can't make a case for earnings to recover, it's difficult to step back in. However, again, if we do see some of these signs that the economic data begins to bottom or even from true green shoots, that's got to help cyclical sectors. It's got to help small caps, especially some of those financials that are in small caps. However, one thing to know with small caps is sense of global financial crisis they've taken on a lot of debt, unlike the large caps space. So again, people see this and they're concerned about the health of some of these balance sheets. You know, we're seeing news out of the loan market, that there's some cracks there. High yield is holding up a bit better. So I think it's a pretty unclear picture on exactly what we get out of small caps. But again, we are actually beginning to see a pickup and activity on both sides of the trade, both TNA and TZA, just because, again, some people are getting very bullish on small caps, where others are just about as bearish as you can get. Now I have to bring you into the gold market because with your hat out here this morning, folks, this is good. This is quite a deal this morning, folks. You know, in the course of half hour, okay, the bottom line is that you had three million ounces of gold sold. That being said, guess what, you know, when we're talking the gold equities and we're talking the nugget or the dust, the bottom line is that it was really intriguing, Dave, we had, you know, gold shoot down a 1448 like in a heartbeat. Yeah. You know, come back to 1456. But it was always not all the time.  But this morning, actually, we were live on the air. It was amazing watching that the first the GDX, okay, you know, bottom line shook it off.  And it's just amazing to me that, you know, we hit 2515. And it said, I don't want to be here. I'm up at 2560 now. So it's like this is almost a disconnect between the metal versus the equity still at this point. Yeah, no, I think that's a good, good and interesting observation, because really, more recently, up until the last couple of days, we actually seen, I've seen the gold mining stocks and gold trading a pretty tight relationship. And we know they're always trade tightly. But yes, the correlation was remarkable. But now we begin to see some cracks in that, which frankly, is probably a bit healthier from, you know, that the equities can behave like an equity and the gold gold can behave like an like bullion. But you know, taking a step back here, you know, gold bullion have been on a pretty nice run up until recently when we have this massive risk on rally. So, you know, my trinity of risk off utility stocks, long term treasuries and gold all hurt last week. But maybe this week, not today, but we'll see if we see a bit of a bounce back and gold. Nice. Well, listen, man, it's always a pleasure for the great education. I look forward to speaking it from two weeks from today, Dave. Sounds good. Thanks for having me back. Thank you. Appreciate it.


If the historical demand for papers was a continuous distribution, in this case the news boy had records that showed that the demand for papers that he sold range from a low of 3,800 up to a high of 5,500. That appears to be a continuous distribution, but it is a uniform distribution and that is a straight line connecting the low and the high. So we need to model it a little bit differently. We don't use the ran function. We use the ran between function. And this is a function added to Excel in 2010, so hopefully you have it. And the ran between function takes two arguments, the low value and the high value. And it returns an integer randomly between those high and low values. It's an integer. You can see here as we calculate the sheet that it returns integers. And that will work for our situation since we don't have fractional newspapers. But in some models you might be working with dollars or something where you need to have decimals. And the way to do that is to modify our ran between formula to give it the number of decimal places we need. For dollars we need two decimal places, which would be 100s. So what we do, we multiply the low end by 100 and the high end by 100 and then we divide by 100. So we cancel out, but that gives us our decimal places. If we needed three decimal places, we would multiply by 1000 and then divide by 1000. So a little trick, but it'll convert the integers you normally get from ran between into the decimals you need for your particular problem.


You got a drink if you don't answer it. Yeah, and if you do answer it, then you don't got a drink That's the rules. I'm so scared right now. What do you guys not like about us? Has anyone ever walked in on you and Steven doing it? Hey! Wait, what? I don't want to take another freaking shot guys. What is the weirdest place you've done it? Oh my god Well, I'm not saying that. Don't say that on camera. I'm thinking. What?  What is one thing you can't stand about the other?  Oh, we didn't want answer what with her twin sister and then we did one with her with my mother And you guys loved them both so we had to bring our Best friends in on it now and do a truth or drink with them to see what the juicy couple questions are Between all of us. Yeah, because they're gonna get juicy. I have some good questions that I want to ask I feel like they're more target towards Madeline because I just I don't know I'm gonna try to target towards Steven. Either way, you got a drink if you don't answer it Yeah, and if you do answer it, then you don't got a drink That's the rules and then on top of that you guys are wondering what the heck is this? What is that? So this is actually white wine, but it's 21% alcohol if you don't know what that means It's strong. It's basically like vodka. So yeah, we tasted it a little bit. We tasted a little bit of this We open this one. You guys know I don't Smell like street vodka one of these would get us messed up So we're just gonna be pouring these into our cups and then from there taking a swing That's how we're gonna do it today Because these are actually stronger than anything we ever had but before we get into this video We also want to say our merch did drop two days ago. No Friday, so Three days ago. Yes, so our merch dropped on Friday. The link is in the description We're filming this before we will actually launch the merch Yeah, we launched it tomorrow, but you're watching this on Monday, so I hope you guys are loving it I hope you grabbed it if you did already.  Okay, also? We do not can don't drinking don't drink We're all of age watch at your own risk So I think I'm gonna start off the question because this the question actually is a really good question for Madeline Oh god, that's that for me. So I'll drink with you So I don't feel like you're eating from She was like toast right now I feel like this is a good question because I've seen this question multiple times So you guys really want to know this has Madeline ever gotten jealous of Mariah hanging out with other girls and calling them her best friend Have you ever felt jealous? No, I can confidently say good I But I know where I stand yeah, she knows where she stands in my life. That's a good thing. Yeah, that's a good thing Yeah, I know yeah, I know that place Okay, what is one thing you can't stand about the other oh this is for both Bill slow-moving as he does it. He does things very slowly, okay He has to sit ready for this video precise. No last night. I was asking for you asking you for an email And he's like no I'm not going to make a new film I just yeah, I poured like half this in here. I was gonna just no you didn't get it right Mariah has a bad attitude sometimes Listen This is all I have to say I say how it is if someone makes me mad. I'm gonna tell you Attitude like no, no, it's just I I don't let people walk all over me And don't let people talk to me disrespectfully So we're basically doing a couple verse couple by the way So only one person from each couple is gonna ask a time so now it's our turn. All right So this next question is for the both of you guys when are you gonna have a kid? We're trying soon.   Oh my god Well, I'm not saying that Don't say that No Yeah, there's my parents Yeah, Bill did drink right before is that a weird spot. It was that normal. That's Hard they didn't ask for detail you can do that Can we end this video please this is The more we drink the worst these are you gonna get I feel like it's already work. That was actually one of the questions I wanted it in darling, but it's okay. I'm sorry Okay, Madeline Steven has anyone ever walked in on you and Steven doing it Anything actually no no like never we never have like a closed call or anything good ever Wow, but I honestly like never Hey, no, well, yeah Have you ever made up an excuse not to do something with the YouTube couple? I'm gonna say what excuse for killing what you just have to say So wait read out that said have you ever made up an excuse to not hang out with a YouTube couple? Yes Why Didn't work out in the way that it was going to work out. So you know, let me just say it's never been any any of our friends It's happened, but not any of our friends like yeah, it's someone that we've never met Yeah, remember Yeah, we were at a party and they want to hang out and if we just it wasn't what you put that in now They know who it was to I would have said yes and moved on like Yeah, he's favorite YouTube couple. Oh Literally we can't wait actually literally what you're pondering it. No, I know I'll make noise I'll make noise That's so weird because I thought okay now mine It is not JD Vlogs before anyone I doubt any people really know that I told you it's nasty I don't want to take this nasty. I'm dumping my whole thing in here.   No No Like our personality come on. No, let me be dead honest.  Okay. No, I'm not my own brain Nothing bothers me I wish you guys could probably say that What a noise what annoys you guys the most from Puffs That's a different question. Okay. Yeah, what annoys me. Yes. Oh wait, it's different question. Yeah, they're asking us What annoys us about that? Yeah? What's me Two shots is already getting to battle Be fully honest, we're best friends here basically like family.  Do I bill is slow-movie? To come Take one night and say that's how he is. He's just slow-moving after that one I Then screw both you guys cuz once again all I want to know what annoys me what it is annoying about me Steve is probably annoyed about how hot Mariah Wait, I can't think of one hang on. Okay. Just drink if you can't figure out. I'm really I don't think so wait, why did you wait that means we would have to drink that cuz we I was I'll see for the last one, but Yeah She's like I was Oh my god, this one is still like Just Oh Well, we got one more so okay. All right, so this is both of our last question I don't know what the score is, but who who's feeling the most tipsy here. All right, so far. I'm pretty I feel like It's 21% I'm telling you that you don't mess around. All right All right, so yeah, Bella's a target to do you can I look at your phone history history and your um Can I look first? Next question All right, only because I don't want Steven seeing the birthday gifts that I've been looking up for That's why that's the one that's the reason why I yeah, I can't believe that This is a loyalty question I'm so scared right now so Marilyn and Steven You ask it have you ever talked shit behind us behind our back Anything even though it's the most I would say yeah I'm sure I've said something. I'm a girl Was it about me, I don't know baby definitely was Mariahs has such a big attitude, I feel like we've all done Yeah, it's just a human nature. Yeah, you're gonna wow Probably like we probably did something like whatever we hang out Wait Just say yes, just say yes, you have yes just to move on. Yes. Yes Okay, dude. I am not Taking one last one to end the video To end the video come on. I don't know who won or who lost but either way it was a funny video Also, make sure you know that our merch link is in the description go copy while you can comment down below Drink dr. I nk letter by letter to get a notification shot in our next video Thank you so much for watching and we will see you in the next video


Well, we were discussing finite and countable sets in the last class. Let us recall again a basic definition namely that we had said that two sets A and B are numerically equivalent and we had used this notation A is numerically equivalent to B if there is a bisection between A and B and then we had said that A is finite if A is numerically equivalent to some segment 1, 2, 3, n, etc. and A is countable if A is numerically equivalent to the that is countably infinite if it is numerically equivalent to n. Countable infinity is same as also as I said some book called denumerable and countable means finite or countably infinite and similarly of course uncountable there is something I did not mention last time uncountable this simply means not countable that means neither finite nor countably infinite or to be more precise it means that there is no bisection between that set and the set of all natural numbers that is that is the meaning of uncountable. Now, the whole question is how does one show that a certain set is a finite or countable or uncountable or anything like that and let us now see some techniques of that in this class. Let me again remind you that in the last class we showed that every infinite set has a countably infinite subset and using that we showed that every infinite set is numerically equivalent to a proper subset and so this is a property which distinguishes between finite and infinite sets. No finite set can be numerically equivalent to a proper subset of it whereas every infinite set is numerically equivalent to a proper subset of it. Before proceeding further let us first observe that this relation is basically an equivalence relation that is something that is fairly easy to see. So, we will see this thing that is first of all a is numerically equivalent to itself that is clear you can take the identity map. Secondly if a is numerically equivalent to b then b is numerically equivalent to a that is also easy to see if f is a bisection from a to b you can consider the it is inverse function f inverse that will be a map from b to e b to a and that will also be a bisection and similarly the so called transitivity if a is numerically equivalent to b and b is numerically equivalent to c then these two things should imply that a is numerically equivalent to c and how can this last thing we proved just consider that is if f is a map from a to b which is a bisection and if g is a map from b to c you consider g composed with f that will be a map from a to c and that will be a bisection alright. Now, this is of course a very straight forward thing to c but what is the great use of this it is the following that if you have shown already that some set is finite and if you know that there is a bisection between a and b it will give automatically that b is also finite similarly if a is countable then b also will be countable or if a is not countable uncountable then b also is uncountable. So, you can use the information about the sets that you already proved using this fact we will see how this can be done now to first of all let us get some working list of countable sets we already know of course that n is countable countable in this case countable infinity and then let us now to prove certain things about countable sets we need some properties of this set of all natural numbers n alright. Now, how does one prove properties of natural numbers n I mean if you want to proceed a very logically you have to start from the definition of n and how n how this set of all natural numbers n is constructed and standard way of that is following what is called this piano axioms it is called piano axioms this is a method of constructing the set of all natural numbers, but that will be very time consuming and we shall not go into that kind of destruction of natural numbers if you are interested I will give you some references where you can find these things, but there are two properties of natural numbers which we shall be using very often and let me list those properties. First is what is called well ordering principle the principle is very easy to state it simply says that if you take any non-empty subset of n then it has a least element so every non-empty subset of n has a least element least element means what that element is less not equal to every other element in that set of course using this property one can show that that least element is unique alright. The second property is what is called principle of mathematical induction of course this is a principle which you have used right from your school days to give various proofs. Now what does this principle say of course you would have used in some form let us let us see in what form we are going to use the principle says this suppose you have a subset of n suppose s is a subset of n is a subset of n and it satisfies these two properties what are the property the first property is that one belongs to s and the second property is that if some natural number m belongs to s then m plus 1 also belongs to s so that is the second property that is n belongs to s implies n plus 1 that is if n belongs to s then n plus 1 belongs to s so if you consider a set satisfying these two properties then what should happen that set s must be the set of all natural numbers then conclusion is this then s is equal to n any set satisfying these two properties must be the set of all natural numbers this is something you have used several times in proving so many things may not been this particular form what is not and we shall be using these two properties of natural numbers these two in in proving that several sets are countable since that is going to be used again and again I mentioned it again you can take this as an exercise actually these two principles are equivalent what it means is that well ordering principle implies this and principle of mathematical induction implies this so I will give that you as an exercise it is an interesting exercise to try show that I will show that one is equivalent to two that means if you assume well ordering principle you can prove this on the other hand if you assume principle of mathematical induction then you can prove well ordering principle I will not discuss that proof here it is a try it on your own if you get held up we shall discuss here interesting exercise on its own now how we are going to use this as I said we shall use it to show that several sets are several familiar sets are countable to begin with let us just start with this by the way why is this called a well ordering principle the reason is the following suppose you let you take a nonempty set let us say a a is a nonempty set then it has a least element suppose you call that element let us say a 1 you remove that element a 1 then a minus a 1 either it is the whole of a or it is still nonempty if that is the case that remaining set also has a least element you can call it a 2 then again do the same thing look at a 1 a 2 either that is the whole of a or a minus a 1 a 2 is again nonempty if it is nonempty then that also has a least element you can call it a 3 so this way you can order the elements of a you can order the elements of a that is why it is called well ordering principle and this is in fact the principle which we shall be using in some of the proofs so in fact in this particular proof which let us what is what does this theorem say it is that every subset of a not not every subset of n is countable we already know that n itself is countable so let us see how this can be proved so let a be a subset of n if a is empty there is nothing to be proved right so if a is empty then a is finite nothing to be proved finite means countable because our definition of countable means finite or countable infinite so assume a is nonempty once you say a is nonempty I can invoke this I can invoke this so if it is a nonempty it has a least element then a has a least element I do exactly the thing that I mentioned just few minutes before that least element I will call a 1 so that least element a has a least element suppose I call that element a 1 now consider a minus a 1 consider a minus this is equal to a 1 right then again there are two possibilities either a minus a 1 is empty or nonempty right so a minus a 1 is empty or a minus a 1 is nonempty if this happens if a minus a 1 is empty what does it mean it means a is just singleton a 1 it has only one element it is a finite set all right so this implies that a is singleton a 1 and is finite what does this imply what will this mean if it is nonempty you again apply the same principle here by this that will have a least element and I will decide to call that least element a 2 so if a minus a 1 is nonempty it has a least element it has a least element and suppose I decide to call that least element a 2 what is to be done after that you consider set a minus a 1 a 2 so consider a minus a 1 a 2 consider a minus a 1 a 2 all right now I will not write everything in the book let us consider a minus a 1 a 2 what are the possibilities here either this is finite or infinite if it is finite we again just say then a is just a 1 a 2 it is a finite set consisting of two elements if not again consider least element call that element a 3 and proceed proceed so this this tells you a technique of how to proceed with this suppose we go on like this what are the possibilities there are two possibilities that is after n steps this may stop then that is a minus a 1 a 2 a n will be empty in which case a is same as a 1 a 2 a n right so then it is a finite set it is it is a 1 a correspondence with 1 2 n if this does not end that means at every stage n a minus a 1 a 2 a n is nonempty you can consider least element of that set call it a n plus 1 and proceed in which case a will be equal to a 1 a 2 n infinite set and that will be in bisection with n so it is countably infinite that is clear so in either case either this procedure if this procedure ends after a finite number of steps it will be a finite set consisting of n elements otherwise it is an infinite set and that infinite set is in 1 1 correspondence with the set of all natural numbers that will be a countably infinite set so it is either a finite or countably infinite which is basically that it is countable that is clear all right now let us come back to this principle which I had said once you prove that certain set is countable anything which is in 1 1 correspondence with that will also be countable so using that fact we can prove the following I will call it as a crawler now that we have proved that every subset of n is countable does it follow from here that every subset of a countable set is countable yeah that is what I said just if you prove something for one set you can say the same thing for any other set which is in 1 1 correspondence with that which is numerically equivalent so I will say a corollary of that is every subset of a countable set is countable now in order to show that a set is countable we have seen that there are two ways one is that you can show that it is in 1 1 correspondence with the set of all natural numbers let me state that here I will only consider the case of countably infinite sets if a set is finite I mean there is nothing much to be proved so consider the set a then I want to say that the following things are equivalent the following statements are equivalent in fact this is something we are going to use very often so there is again a very standard notation used for this it is this t f a the following are equivalent we will just use this t f a to show that the following are equal since we are going to use it again and again we will use this standard notation and it is fairly common it is used fairly often also and what is that first I want to say that a is countably infinite then there exists a subset b of n and a map f from b to a that is on all right and similarly we can say that there exists a subset let us say c of n and a map so we are called g from a to c map g from a to c that is 1 1 what does it mean that these three are equivalent that is and what is the practical use of this theorem that is if I want to show that a set is countable we have seen earlier that by definition I should say that there exists a 1 1 correspondence from a to n but what this says is that in fact one can show something less for example it is enough to show that there is a map from a to some subset of natural numbers which is 1 1 right that is enough there is we can show g is there is a map g from a to c not not dc this will mean complex number a to c that is 1 1 or you can find a subset of natural numbers and find a map from that subset to a which is onto that is sufficient that is sufficient all right now first of all it is clear that 1 implies 2 and 1 implies 3 you can just take that subset as the set of all natural numbers itself you can just take this b is equal to n and then there is a map from n to a which is 1 1 and onto and so in particular onto similarly here you can take this csn you can take this csn so real issue is to prove that 2 implies 1 and 3 implies 1 to show that see right let me just write 1 implies 2 1 implies 3 obvious clear right so the issue is to prove 2 implies 1 and 3 implies 1 all right so we need to prove 2 implies 1 and 3 implies 1 since 3 implies 1 is easy I will take that first what does this say that there exists a subset c of n there exists a subset c of n and a map g from a to c that is 1 1 right that is there exists a subset c of n and a map g from c to a that is 1 1 only thing is that this map may not be onto only thing is that this map g from c to a may not be onto but does not matter see instead of I can I can consider no I think I not c to a a to c a to but what we can say is that even if it is not onto onto n we can consider this g of a we can consider this g of a then a to look at the map a to g of a look at the map a to g of a we already know that it is 1 1 and since we are not we are taking only the elements of g of a that is onto we are taking only elements from a to g of a that is onto. So, a and so what it means is that a is numerically equivalent to g of a right is numerically equivalent to g of a all right is this g of a subset of n right its subset of n now look at this theorem every subset of n is countable we have already shown every subset of n is countable. So, in particular this g of a is countable and hence countably infinite because it is not finite. So, it is infinite so it is countably infinite that shows that a it is countably infinite fine in a similar way you can show that 2 implies 1 because what we can think of is the map which takes f from b to a that is is this clear first of all 3 implies 1 it is enough to just consider a subset of a natural numbers and show that there is a map from a to c that is 1 1 and similarly it is enough to consider a subset of b of n and show that there exists a map b to a that is onto right. See what you can do is that you can see the map again similarly as we have followed here the map from b to a is onto it is not 1 1, but what we can do even if it is not 1 1 from b to a I can think of a subset b of a and a map from b of a which is both onto as well as 1 1 and in that subset is countable and how to consider that map from b to a which is 1 1 and onto either you can take either you can use axiom of choice or you can use well ordering principle that is you can take that is you look at an element a consider it is inverse image in b that will be some non-empty set if that is a subset of just 1 element there is no problem if it contain many more elements you choose the least element of that and do it for each element in a that way you will get a subset of b which is in 1 1 correspondence with a that will be a subset of natural number I have given you the main idea you can develop the proof with this. Now, we just consider one more extension of this instead of considering a subset b of n that is what I want to do is that I want to replace this n by any countable infinite set right instead of taking n I can say that there exist subset b of some countable set and a map b from f from b to a which is onto. So, again by the principle which we thought of just now this is similarly I can consider any other subset from a to any subset c which is instead of taking subset c of n I can take any countable set and say that there exist some map from a to c that is 1 1 that will be enough that is enough right and this is a principle that we are going to use to show that several well known sets are countable or not countable. In fact, this will be used to say that they are countable. So, first of all let us just take an illustration of this I want to say that n cross n is countable and of course, since it is easy to say it is infinite we shall show that it is countable infinite n cross n is countable infinite I will use this 3 if I am able to say find a subset of natural numbers and a map. So, suppose I call this a is n cross n if I am able to find a subset of natural numbers and a map g from this set a to that subset c which is 1 1 that is enough right what are the elements of n cross n yes ordered pairs of the natural numbers ordered pairs of. So, n cross n this is the set of all elements of the form m comma n where m and n both are natural numbers. So, I consider a map let us say g from a in fact I will take this set c as n itself. So, I will take a map a g from a to n as follows define g from a to n as follows g of this m comma n g of this m comma n I will take this as say 2 to the power m into 3 to the power n. So, this is a map from a to n that is ok is it 1 1 see how does one show that something is 1 1 see suppose you take some other m 1 n 1 then g of m 1 n 1 is 2 to the power m 3 to the power m 1 3 to the power n 1. So, if let us say we consider g of m 1 n 1 this will be 2 to the power m 1 multiplied by 3 to the power n 1 suppose these 2 are equal g of m n is g of m 1 n 1 then that means 2 to the power m into 3 to the power n is same as 2 to the power m 1 into 3 to the power n 1 will it follow from that that m is n is same as m 1 n 1 that is suppose these 2 are equal then that will imply that 2 to the power m into 3 to the power n is same as 2 to the power m 1 into 3 to the power n 1. So, what I can say from here is that this will imply that 2 to the power m minus m 1 is same as 3 to the power n 1 minus n, but some power of 2 is equal to the some other some power of 3. So, when can this happen this only one way that this can happen that is that must be 1 that is if this is to happen then this must be equal to 1 that means m minus m 1 is 0 and n 1 minus n is 0 which is same as saying that m is equal to m 1 n is equal to n 1. So, does it prove whatever we wanted to say we have found a map from n cross n into n which is 1 1. So, that is does it show that n cross n is countable that is that was our 3 that was our 3. What if I take n cross n cross n I can say I can take a map to 2 to the power m 3 to the power n. So, let us something like 5 to the power something and what is the most general statement I can take a finite number of times countable product finite number of times the product of that is n cross n n cross n finite number of times in other words product of n cross n cross n taken finite number of times is a countable set. And all that what is what is so peculiar about this 2 and 3 it is just that they are primes it just that they are primes you can just choose a finite number of primes and construct a map like that. So, a product of a quotation product of n taken with itself a finite number of times is a countable set. In case the infinite number of products. Yes. Infinite number of products. No, we will come to that later. As far as finite. So, Cartesian product of a finite number of copies of n is countable. So, this is a theorem here this corollary is that I can replace n by any other countable set. In other words if I what I want to say is that suppose if a 1 a 2 let us say a k are countable sets are countable sets a 1 cross a 2 cross a k is countable. In other word if you take a finite family of countable sets then and then take the Cartesian product then that is countable. Does it follow from here all that we are doing is replacing n by any countable set each of this a 1 a 2 a k is equivalent to n and so replacing n by all that. Let us look at the union and in union we can take even a countably infinite family. So, let us say that let a i i belonging to let us say n be a family of countable sets a be their union a b equal to union of a i i belonging to n then a is countable or to put it in words if you take a countable family of countable sets then their union is countable that is union of a countable family of countable sets is countable that is what we say in words. The proof is very simple we can view this union a as a subset of n cross n we can view this union as a subset that is in other words we can establish a 1 1 correspondence between a and a subset of n cross n and since we have shown that n cross n is countable every subset of it is countable and hence that is countable. And how does one show that let us look at the set a 1 we know that a 1 is countable. So, it is finite or countably infinite. So, it is either finite or it is in verbal correspondence with n. So, suppose it is finite I can write its element as let us say a 1 1 a 1 2 etcetera. If it is finite it will stop somewhere if it is infinite it will continue it will be in 1 1 correspondence with n and similarly for a 2 I can write elements of a 2 as a 2 1 a 2 2 etcetera. If it is finite it will stop at some stage a 2 n otherwise it will continue and do it for any i. So, a i will be a i 1 a i 2 etcetera does it more or less finish the proof. Now, a is union of all this a i's and so I can write a as nothing but the set of all elements of the form a i's a because if you look at take all of them all elements can be expressed as a i's. And can you see an obvious map from this into this set n cross n. For example, I can say that you take a map f from a 2 n cross n what is the map a i's a goes to i comma j a i's a goes to i comma j. So, that map is 1 1. So, a is in 1 1 correspondence with some subset of n cross n and hence a is countable. We do not have to show that it is on to we already seen that it is essentially we are using this principle 3. So, let us again recall what did we prove so far that if you take any now let us go to some familiar sets go to this set z is the set of all integers. What are the elements of this they are all integers. So, what are so they are let us say the first is set of all natural numbers. So, what are the extra elements other than this d 0 this I will say this union 0 union minus 1 minus 2 etcetera. This is any way a countable set we know already this is a finite set what about this this is a in 1 1 correspondence with n it is a countable if it is. So, this is a finite union of countable sets this is a finite union of countable sets. So, it is countable. So, now we have got how did we begin we wanted to discuss how to show us that certain set is countable or finite. So, after proving these theorems we have now found one more technique. So, what were the techniques that we showed so far either you can show that it is in 1 1 correspondence with n or with some subset of n or with some set which you already shown to be countable and now we have got one more technique namely suppose you are able to show that it is a union of countable sets either finite union or countable union of countable sets then that is also countable. So, this is now one more technique to show that some set is countable you can show that it is a union of countable sets either finite union or a countable. In this case we have shown that it is a finite union of countable sets. So, z is countable so z is countable. So, z minus equal to 0 that is also countable. So, now suppose I take the product cross product z cross this that is also countable set. Now, can you see that obviously this is look at the set set of all rational numbers set of all rational numbers now what is that set by definition it is the set of all elements of the form p p by q where p q are integers and q dot 0 that describes all rational numbers that describes all rational numbers. Does it follow that this is countable because we have seen that this there is obviously the relationship between this and this set there is only one problem here this representation p by q is not unique 2 by 3 is same as 4 by 6 that is same as 8 by 12 etcetera. But that is not a problem we can see that once so that means you have a map which goes from here to here I can say that I can take the map p q goes to sorry p q goes to p by q that. So, map from here this to q this to q that map is on 2 but may not be 1 1 that map is on 2 but may not be 1 1 because as I said just now this 1 3 2 4 they will all go to the same rational number. But we have seen that that is not a problem you look at the statement 2 of our theorem if you have a map which is from a countable set which is on 2 but not necessarily 1 1 still this set is countable in other words we can q we can say that q is in 1 1 correspondence with some subset of this q is in 1 1 correspondence with some subset of this and since we already shown that this is countable all its subsets are countable. So, the set of all rational numbers are countable is clear now before proceeding further I will give you one exercise. Let us to take that consider exercise we need a definition of what is called an algebraic number have you heard of this earlier what is been an algebraic number does not matter we will define it a number is set to an algebraic number if it is a root of a polynomial with integer coefficients. So, it can be a real number or a complex number so it is called so let us say that z is a complex number it is set of so z is called an algebraic number if z is a root of a polynomial if z is a root of a polynomial with integer coefficients with integer coefficients which is same as saying that means polynomials means what polynomials is a polynomial is a function of the form a naught plus a 1 z plus a 2 z etcetera all that now what we what is it all this a naught a 1 a 2 plus b integers. So, what we can say is that if there exists let us say a naught a 1 a n belonging to z of course all of them should not be 0. So, let us just say a n is not 0 that a n is not 0 and what should happen is that this z be a root of the polynomial that means a naught plus a 1 z plus etcetera that is a naught plus a 1 z plus a n z to the power n this should be 0 is a root of a of course if you take all of them to be 0 then it will mean that every numbers will mean. So, we do not want it that is why we take non-zero polynomial and one way of ensuring that a polynomial is non-zero is that at least one coefficient is non-zero we shall ensure that a n is not 0. So, this covers everything now how do we how do we know that certain number is algebraic or not. Obviously, all integers are algebraic numbers we can just we can just take the polynomial for example, if you take the number 2 I can consider polynomial z minus 2 it is a root of that. If I take root 2 I can take z square minus 2 and it is a root of that it is a root of that. So, root 2 is an algebraic number now to decide whether a particular number is algebraic or not is not very easy for example, in case of root 2 it is fine, but suppose I give a number like e or pi you cannot say easily whether it is a algebraic or not. In fact it is not they are not algebraic numbers, but that is fairly difficult to prove. Now, what is the problem? The problem is this show that this set of all algebraic numbers is countable that is the problem show that show that the set of all algebraic numbers is countable. I give you a hint I will not give the full solution I will just give you a hint what are the ways of showing that a set is countable? The most recent way that we saw is you can show that it is a union of countable sets or union of finite sets whatever. So, I will say that you try to show that this is a countable union of finite sets you can show that it is a countable union of finite sets. So, now we have seen so many examples of the sets which are countable which are countable that is finite or countable in fit. Now, this may raise a question whether there exist uncountable sets or not whether there do exist uncountable sets or not and that is something that we shall answer by now how does one show that certain set is not countable? By definition you have to show that there is no one one correspondence between that and the set of all natural numbers that is one way of showing and then once you show that some set is not countable then any set which is numerically equivalent to that is also not countable how to go about showing that we shall we shall discuss that in the next class. We will stop with this for today.


Hey guys, it's Alex here from AlexVegas.com today. I am going to unbox the Juve the Juve Mini so this is the mini combo device with 660 nanometer and 850 nanometer light And I'm gonna unbox it. We're gonna set it up and look at the size and everything like that and See how easy it is to use. So let's get started. So the first thing in here is this little box which has a really handy Timer, okay, so if you've seen my videos, I've got a few videos reviewing the Juve Original and also the Max so be sure to check them out and also a comprehensive review at AlexVegas.com I actually really like this. It's the first time I've seen a black one The other ones I've had have all been silver ones, but it's actually really really useful because what you can do is you can just set the timer so Let's say I want a four minute cycle we had start counts down Simple, right? But it's got a magnet on the back. So it'll attach to the device. It's um, it's actually really really handy. So Instruct the menu in there as well. Not that you need it. And then of course we have the device itself So what do we get? So this was $5.95 Think about $600 a little bit under 600 us for this device By the way, if you use code AlexALEX my first name you will save a little bit. It's a coupon code there So this is the smallest one they offer and again, I've got videos on the original the original is five panels Boxes or whatever you want to call them Of lights the mini is two and the max is I'm just looking at it now two four six eight ten twelve It's about 12 one two three four five six seven 14 panels. So yeah, this is the tiny one and we'll do a comparison with the bigger ones soon So I mean this is really useful If you're tied on space or obviously on a budget Um, I plan on using this more for my head and using the max for the full board That's the the panel. We'll do a close-up with this now. So You can see here two two panels and then on the back We have the two fans Some rubber stoppers here and then on the top On the top We have the screw on bolts so we can hang it up and on the bottom We have the power plug and the switch Okay So it also comes with this little booklet which has Frequently asked questions how to set it up little bit of an overview reviews What else? Distance and time how to use it and the technical specs All right, so this one is the 660 plus the 850 nanometer which will mean when I turn it on It will look like some of the lights aren't working Because that's scenario for it All right, what else we got? so these So these accessories That's a door hinge so you can hang it from a door.  This is a adjustable height pulley so you can Lower it or hide lower it or lift it These screw into the top of the device here Then we'll get a power plug So what I'm gonna do is I'm gonna sit this up and I sit this up and then we'll go hang it I'll show you how it works see this Magnet, sorry dude, it's cool. So what I'm gonna do is I'm gonna sit this up now and Show you how it works when you're hanging it on the wall hanging it on the door and that sort of thing So sit-ups really easy it comes with these Middle cables that you literally just Screw onto the top Like so there's two of them and then use this Carabiner connect those together All right, once that's all screwed on you can go hang it wherever you want to hang it And we can use this pulley and also the door frame support. So um, let's go do that All right, so I'm here on the wall. I've got a nail up here got this little pulley system I'm gonna use that for the panel here with a clip on it. It's going to Hook that on like pulley system To lift it up. So that's useful if like I want to hit different body body areas different heights Again, I can easily Pull it up just by using the pulley just lifting the the device Pass which is on the bottom. Let's go plug it in So I've got the power cord here. It's pro. I don't have a tape measure, but it's it's probably about I Don't know two and a half meters three meters, which is six or eight ten feet long So you got plenty of length on there. I live in New Zealand. So this plug won't work I need to get an adapter so that's something to keep in mind if you Don't live in America and you buy one of these because they do ship glimmer So I'm gonna plug this in fire it up and then we'll go put it on the door and that's it That's that's the many fire and so you can see this is the combo So if you just got all 660 all the lights would be red if you just got the near infrared You wouldn't see any of the red light. It'll be the near infrared which is not visible to the human eye Um, I forget the combo, of course, it's gonna look like that.  So, you know females might want to use it for like skin rejuvenation rejuvenation struggling with that word you know things like that so It's good device a good size. However, um from a dollar point of view you better off spending a few more dollars and getting a much bigger one So I'm gonna hang this on the door and then I'm gonna compare it to the other ones that you might be seeing across my shoulder So unfortunately the door bracket that comes with the juice Doesn't fit on any of the dollars that I have in this older house I don't know if it's just like a New Zealand thing, but a lot of the doors here are really thick Like toothache for this to fit on so I'm here in the laundry We've got some cupids, and I'm just gonna hang it on a cupboard to demonstrate how it would work if you were using it on a door so This bracket, which is well over an inch thick, but obviously not thick enough for my doors would just sit on the top of the door like so and then you take the juice and hang it Like so simple as that Obviously if you didn't want it that low you could get rid of the pulley set up all together Which is actually quite hard to do one handed Okay, so you could just hang it directly on a fan like so and you don't have the pulley system Plug it in and then where you go. So that would be good to put on the back of doors You know cupids and stuff.  You can hang it up on the door Do you five ten minutes each morning? You know after you've had a shower when you're getting ready? Use it at night. You know put in the bathroom. I think it'd be handy in the bathroom You know when you when girls are doing the hair or the makeup or whatever Probably not the best for makeup. It's gonna Like change the colors a little bit But do you know what I mean? You brush your teeth at night and you got a red light there just on your face We know red light helps with the collagen production and we're healing all that all that sort of good stuff Which by the way, I've written about that so I'll put some links in there and the notes below so you can check them out So yeah, that's the juju mini what I'm gonna do real quick before we finish is compare it to the other one So let's go to that Alright, so you can see the three juice panels here with the max the original and then the mini So you can see how much smaller it is I don't want to go too detailed with the comparison in this video because I do have a separate video that Does a full analysis on the difference between the more cost benefits on it So be sure to check out that it's on YouTube You'll see it pop up somewhere But yeah, hopefully that answers the questions about the juice mini which I have here Just under six hundred dollars US use code Alex al ex to save a few dollars when you order if you have any questions about this device just post them below in the comments section and I'll happily answer them. There's something that you want to know like how heavy is it? I don't actually know the weight, but I mean you can see me here pick it up one handed I couldn't do that with those because I quite heavy You know if there's anything that I haven't answered feel free to post the questions below and I'll do my best to answer them Practical applications for this We've covered a few already, you know the bathroom back of the wardrobe This is you're getting a ton of red light that reason why I like the jubelites is they're very powerful Unlike some other red lights on the market So you know you're getting a good dose of red light and you don't have to stand in front of it for a long period of time MF levels are really low as well. I've done videos testing the MF so you can be you can go check out them on YouTube So it's really good device and we know we're getting red light from it the good thing about this is I Mean it's it's it's bigger than like some of the small handheld lights I have here So you get more coverage, but when you compare it to those ones, you know You're not getting your full body coverage So this would be good for someone who's on a on a budget and just can't stretch the budget to the bigger one or doesn't want to use the financing or Just once a small area, you know, maybe they just want to focus on their face or You know in the stomach or something equal for injury for me what I plan on doing with this is What I actually want to do is I want to use all three have the max in front of me the original on the side And then this one may be like above my head So it's coming down on my head See if I can get some hair regrowth and then just Just sort of saturating the body from the top down if I didn't do that if that was too difficult Maybe I could use it around my feet You know beneath that one just so you've got an extra layer Extra extra few inches on there. So anyway, if you have any questions about this one Let me know if you want to save a few if you want to order this and save a few dollars use code Alex And you'll save a few dollars I've also got a review and an emf test of the original so be sure to check that out I've got an unboxing video of the max So be sure to check that out and I've got a full comparison video of all three so be sure to check that out hit like subscribe and Send through any questions