Finally, it's in my hands. This is Christian Daniel's follow-up to their Fernando Chelsea boot. This is the Larry Layser boot. Here are my first impressions. G'day. Welcome to Bootlossophy and I acknowledge the traditional custodians of Wodget Country, which is where I live. Now, for those of you who don't know, Christian Daniel as a brand only started in 2022 when they launched with a kickstart campaign for their Fernando Chelsea boot, which I've got in black here. They also came in maple and I chose the Dr. Sol, a half Sol, because I didn't have any at the time. So, what followed this came their Larry Layser boot. This is in Wicked and Craig's Russet Leather, which I'll tell you a little bit about, but it's still made in Leon in Mexico. Now, I'm unclear whether or not Christian, from Christian Daniel, has actually still contracted to a factory or he's actually brought manufacturing in-house, which is his intention. But whichever it is, it's still currently being made in Leon in Mexico. This is their second model, as I said, the Layser Larry boot. It's available in this Wicked and Craig Russet Leather, as well as in a Buck Brown VegTan Leather. I'm not sure the tannery of that one. But let's have a look at what's in the box. Now, obviously, I've already opened the box, but what came with it, apart from the boots, were a couple of business cards from Christian Daniel and also from Dale's Leatherworks, because included in the package is a cuff from Dale's Leatherworks, as well as the key ring from Dale's Leatherworks. So these are great little free gifts. And on top of that, the boots came in plastic bags. I'm not quite sure about that, because I think sometimes they might sweat in the plastic bags, particularly they go through hot countries. But they came in plastic bags inside these Christian Daniel cloth boot bags, which are, I think, really great quality. They're little tassels in the pull strings. So that's what came in the box. Now, let's take a look at the boots themselves in my first impressions. So let's go through the components, which are listed on the website. Now, I haven't had time to do enough research for them, because I got these a few days ago, and I've been wearing them for a couple of days just to see how they feel and where they're in. And I'll tell you about that in a minute. But the components, which I'll read off the website, are the construction is available in 270-degree stitch down or 270-degree Goodyear welt. These are the 270-degree stitch down model, which I chose. The upper, in this case, is russet, that's the color, traditional harness from Wicked and Craig. That's a veg tan leather. And my understanding is that Wicked and Craig is the last remaining only veg tan tannery left in America. I have a belt made of this harness leather, much thicker obviously, and it comes initially as a sort of pale natural color and darkens to a very light honey. It doesn't get much darker than that, I don't think, because I've been wearing the belt for what is it, a couple of years now, and it hasn't darkened all that much, it's just become more supple. So I expect these not to darken tremendously, but I was surprised when I saw it because I thought russet might be an autumn leaf kind of color, reddish, but these are obviously, as you can see, quite a natural color, not as pale, mid sort of level brown as a brown chromic cell, as natural chromic cell, but in the veg tan it has that sandy sort of color. What else? The insole is veg tan leather, the midsole is veg tan leather, the laces thin round cord color matched from guarded goods. So these are my first guarded goods laces, that's interesting. It has a steel shank to give it arch support and stability down there. The outsole is a vibram etan outsole, which is very similar to day night. I mean it looks like day night, but the rubber composition I actually like. I think these are my first etan soles from vibram, and I find the shock absorption on this and the grip quite a bit better than original day night. It's a little bit softer in composition and because of that I think the grip is a little more secure and it's completely resolvable because it's either stitched down or a good year well done. First impressions, I'm impressed by the wicket and craig veg tan leather. It's actually quite thin in the boot, it's less than two millimeters and because of that it feels really quite supple in the shaft, it's unlined in the shaft and lined with leather in the vamp area, which makes it a little bit more, a little less soft and supple in the vamp than it is in the shaft as you can actually see, just for a few days where I'm already starting to roll the leather in the shaft as it as it groups my ankle and fits me. It's a broke pink cap toe as you can see, it's got the pinking and the broguing and it's stitched down. I don't believe it's a real cap toe, I think there's a piece of leather that comes down the vamp and then the cap toe. It has I believe a thermoplastic toe puff, although I think it has a leather heel counter, can't be sure about that. Single piece heel counter, heel backstay, which I think makes it look quite elegant. All brass eyelets, quite small actually, they're not huge eyelets which again makes it reasonably dressy. It's clearly a service boot, slightly less than six inches from the top of the shaft to the top of the heel. You can see the midsole is leather all the way through and the stacked leather heels that's leather as well. The stitch down is actually done very neatly, the stitching is extremely neat and the layer of the vamp that comes down and falls over to be stitched down is also lasted very neatly. The stitching goes through the outsole, double stitch there and then a single stitch continues to the heel and as you can see the heels are actually also nailed in. Construction wise I think it's very secure. There are a couple of loose threads if you're looking for that sort of thing. I point them out but who actually looks at loose thread like that? I don't know. What do you do? Run a magnifying glass over your boots every time you put them on? They don't come apart. Structurally there's sound and if there's a little thread like that you can do two things. You can burn them off, forget about them or you can write on your Facebook post and complain. The Wicked Craig leather is actually quite soft. I just accidentally ran it across my office chair and I cut it. It's not a huge particular problem. Interesting thing which also happened on my Dublin boots from Oak Street Bootmakers. They crease a little ununiformly. The right one creases on the vamp more than my left one and I just think that happens to be which part of the hide is being used per boot. The feel of it is really good. I'll put them on feet so you can have a look but the feel is pretty good, pretty comfortable. Yes there is a bit of break in required to get it to flex where your foot bends but otherwise there's not a hell of a lot of break in required. Certainly not on the uppers. Let's get them on foot and we'll have another talk. The laces are actually quite long and quite waxy from guided goods.  So the fit. Christian Daniel recommends going true to size. So I'm a US 8.5D in my brand size. Usually with American boots I'm wearing US 8D. In the Fernando which I'd got earlier I went true to size and the 8.5D fitted really well. Strangely enough in these they're a little bit bigger in feel than the Fernandos although I also went true to size and took 8.5D. It's the same last so I can't say it's due to the last. I think it might be due to the lasting on the leather because the Fernando I think is in Lafax Elbratos leather which is very similar to Chromic Cell and so a bit stretchy. So when it's pulled over the last I think it might stretch a little bit more and then when the last is removed it relaxes a little bit. Whereas with Wicked and Craig's VegTan leather I think it has a firmer temper which means when you last it it's not going to stretch a lot. So when you remove the last it sort of relaxes back into a slightly larger shape to it. So it there might be a difference of maybe one or two millimeters but it's enough to make me feel like in these I need to wear some thicker socks. I'm wearing dress socks at the moment and I have worn them with thick boot socks and they feel much better. As you can see it's very flexible. I'm not getting any resistance or much of a heel slip. I've already worn these I think about two days it might be two and a half days. So there is there has been some slight break in already but I have no heel slip. I just did not find any heel slip from the beginning when I put them on out of the box. They're very comfortable. They're very roomy. The feel under my foot is some pretty darn good shock absorption. So the cork filling the leather that's used and the etan sole from Vibram I think are really good in that respect. Heel strike is very comfortable so I have no complaints there at all and the arch support is actually really quite good. Comfort I would give easily 10 out of 10. Perhaps not as comfortable as really well-built orthotic shoes like the Old and Indy but 10 out of 10 in my feel. Okay let's sum up. So now to value. They sold for US $475. Now that compares that sort of price range with Oak Street bootmakers and Truman boots and they are a bit more than Parkhurst and about $100 more than Grant Stone which as we know has economies of scale in China. That's a difficult range to market I think because it's quite a busy price bracket in terms of the brands that are there. Truman I think honestly are built more sturdily than this. They just feel a lot heavier I think there's thicker and stronger leather components in the sole and they're heavier than this is and it just feels a lot more sturdier and also bear in mind they're made in the USA Truman boots and hence have USA labour costs. The quality I think is comparable to Oak Street bootmakers and Parkhurst as well. They're in that sort of lower range between the 300s and the 500s although this is in that above 400 range. So look in value terms it's artisanal made yeah okay it's handmade artisanal it's not in the factory what I mean by that it's not in a line factory where there's loads of people and you know the boots go through the line they're actually made by artisans on a bench. It's a small batch manufacturer so it's difficult to get economies of scale but I think overall you'd have to say that probably at $475 it's a bit on the high end of the acceptable scale. I think it's acceptable I think if you like this type of boot and particularly if you want to support a small brand manufacturer this is this is acceptable but you have to say that if you look at Parkhurst let's leave out Grandstone if you look at Parkhurst Truman Oak Street bootmakers I'd say this is this is in the same price as Oak Street bootmakers and probably the same quality build but Parkhurst I think is the same quality build but lower Truman is probably more sturdy and in that price range so value acceptable so there you go that's my quick first impressions of the Christian Daniel Larry boot I actually like it a lot a lot because of the comfort of the wear and I will keep wearing this at $475 I am prepared to invest in a new small brand and if you like your boots I think you should as well particularly as this fits quite well as I said it's a it's a true to size at 8.5 D for me the the last is quite comfortable in this case a little bit roomier than my Fernando boot and I guess one of the issues that you're going to find is that it is a group MTO and then you kind of have to wait for a while in order to to get your boot from when you order so it's not available off the shelf but if you're interested in it get on to the website and sign up and when the next group MTO comes along you can grab one of these at the moment they've offered these no Fernandos but I'm guessing that as Christian raises capital through his profits he'll start to offer both in their MTOs so in summary I like them I like them I think they are worth it although at the at the higher end of that price range for acceptability very comfortable and I'm gonna wear these with with a lot of fun so that's it I hope you like the review if you know you know what to do click on like and if you're watching this and you haven't subscribed yet please do why not so stay in touch click on subscribe so that you know when the next video is up and look after yourselves and I'll see you soon


A Red Bee man charged with killing his one-year-old son made another appearance in federal court today. 24-year-old Gary Wayne Jackson Jr. is charged with murder and is accused in the January 2nd death of his son, who died from blunt force trauma to the head, according to the criminal complaint. The death happened on the Red Lake Indian Reservation. That's why it is being prosecuted by federal authorities. According to the complaint, Jackson told his mom in a text message that he hit the boy but didn't want to hurt him like that. Jackson later told the Red Lake police officer that he thought he killed his baby. At today's court hearing, Judge John Huesby granted a motion by prosecutors to keep Jackson in custody until his next court appearance. That court appearance is scheduled for St. Paul on January 12th. If you enjoyed this segment of Lakeland News, please consider making a tax-deductible contribution to Lakeland PBS.


Hey guys, this is rich from rich to be live. So I wanted to show you guys genius brands website. This is what it looks like pretty cool Cartoon cartoon channel fun for kids safe for kids free for everyone You could find them everywhere like on all major social media platforms and Streaming platforms and then when you go to our brands you can see all the different brands But this is the one that I'm really interested in obviously as an investor You could see right here Warren Buffett's secret millionaires club and this is the video I was telling you about yesterday and the music they're playing check this out listen to the song Friends and our family say remember kids the best investment you can make is an investment in yourself and today that means practicing safe and hygiene So this is one of the reasons why I really believe genius brands has a chance to be huge guys this Brand here not only do they have baby genius which when my kids were babies they love these products and We actually purchased many of these products for our children and I'm sure if you're a parent you probably have purchased these products too So these guys have been around for over ten years with baby genius and now they're getting into so much more And I love what they're doing with Warren Buffett and the secret millionaires club I can just imagine kids love them watching this check this out I'm Warren Buffett and the last year or two. I've been working with Andy Hayward on a on a series for young children called the secret millionaires club and I was enthused about this project when we started and And far more who's even about it now are basic messages that the best investment you can make as an investment in yourself We put this in an entertaining form so that Young people are watching if they're enjoying themselves, but they're also Picking up the lessons of life that will make them more successful and happier people Please call the meeting order That's the pick guys and that's what the reason is why I think this is going to be a great pick secret millionaires club genius brands international Stay tuned


Back to the metal voice. All the way. Hey, Jimmy. Firewind guitarist, Gus G, solo artist. Guitarist extraordinaire. We'll show you some. Okay, Gus, where are you right now? I am in France right now. We are playing in a city called Savignilet Temple, which is right outside Paris. And I'm sitting on the tour bus. I'm at the front lounge of the bus, finished soundcheck, and the show is in a few hours from now. Do you speak a little French? Do you not? No, I don't. I can only say merci. Well, that's good. It's good. That's good to do right after the show, right? Merci beaucoup. Merci beaucoup, that's all. That's good. All right, so also the new album, Hasbro released two great reviews. The Firewind Stand United, it was out on March the 1st, just released a lot of good, positive critique about it. Maybe you want to just quickly give your feedback on what you've been hearing so far. Sure, yeah, the album came out last Friday, March 1st. You're right, the reviews and feedback so far is incredible. Honestly, I mean, we've been doing it for quite a while now, it's the 10th studio album. So I don't know what to expect anymore. And I don't know what it means if you have better or worse reviews, but it's an indication, but the feedback from both from press and our fans so far is incredible. And we're playing a lot of new songs on the set and all the new songs go down so well. So I'm happy, you know? We put a lot of work into it. Yeah, I'm happy for you guys too. So right now you're in France and just tell me a few more dates that are coming up. Any other countries in Europe? Right, yeah, we're doing, we'll be all over Europe until March 24th. You know, we just did Germany and Holland. We are gonna do, oh, where else? Austria, Slovakia, we're gonna go to Spain and then Scandinavia a little bit. We're gonna play four shows in Sweden, two in Norway. And then we're, you know, crossing the pond. We're going over to North America. That's nice. We have the US tour, yeah. So it's gonna be a tour that's gonna take us all the way to the end of May. After America, we go to Japan. So everything is lined up very nicely. You know, it's just a little bit of a nightmare to get all the visas together, but we're getting there. I remember last time in North America there was some issues, but. Oh yeah. We did it. So Firewind's doing Europe and we're in North America and all the dates, you could find it on what Firewind website.  All, because I'm mentioning this because that's where all the dates and all the direct ticket links are there. So people that wanna come out and see us, they can go there. So yeah. All right, cool. Also the big news, like actually for me, it's big news, right? I texted you. For me too. Maybe like 10 minutes ago, I texted you. Yes. No way. So you posted on social media that you revealed on social media to the masses, we'll say, that you played lead guitar on Eternity Has Failed on Bruce Dickinson's new solo album, The Mandrake Project. So I'll talk to you a little. I go, Gus, we gotta talk about this. So I go. Yes. Van, just call me, okay? So here we are.  Like now that you can talk about it. Yeah, sure, sure. You know, this came through my friend, Roy Zee, who's Bruce's right-hand man for many, many years. And, you know, he's his producer and they co-write together and everybody knows who Roy Zee is and how important he has been to heavy metal world. But yeah, you know, I've known Roy for a long time. I've known him for 20 years. I worked with Roy before on Rob Rock's album. Anyway, so we've kept in touch. We actually toured together before as well. He was in Halford's band and they were out on tour with Ozzy when I was in Ozzy. So we toured together. Anyways, so. No, it's good to have some background. That's cool. Yeah, just to give the background that, you know, because me and Roy are friends and go way back and I knew he was working on this Bruce album for a long time. And at one point he reached out and said, dude, I have this, you know, we're doing a song and I would love to have you on there to do like a guest thing. And we can like trade leads.  And actually I recorded this solo about a year ago. Wow. Actually. So it's been a while, you know, that I did the tracking and I was actually on tour at the same, at that time as well. I wasn't like here now on a bus, you know. It was a day out. We were on tour with Beast in Black at this time last year. Yeah. And it was during a day off that I went into a hotel room and set up a small home studio and Roy sent the track over and I just did my lead guitars there and I sent them the tracks back. And then I didn't hear anything for months. That's how usually goes. You do a session and then you don't hear anything for months. I should plug this. I should plug this as we're talking. There we go. Roy Z, Bruce Dickinson and yes, the parents like us. Go ahead. So yeah, man. It's a great album. I didn't, the thing is I didn't hear the final thing until it came out a couple of days ago as well. Were you pleased? Oh yeah. Oh yeah. I mean, the production is incredible. It's a great album. We love the production. Love, there's like so many layers, so many things to it. Bruce's singing is man, top notch. Yeah. Yeah. And yeah, I mean, that song and I heard it and it's like all these, it's a long solo part. It's about two minutes long. And you know, we trade leads with Roy and I'm playing a lot of the backing melodies as well during the solo section. And there's like a keyboard lead by Mysteria. So it's cool. It's epic. It's an epic track. I'm honored to be part of it. You know, Gus, I think this track is actual. So for everybody who doesn't know, this was written for Bruce's solo album originally, then Iron Maiden sort of made it their own little version. And now it's back as a solo piece for Bruce. Did you listen to the original and saying, you know, I want to keep this or like, did you listen to the original solo and say I want to preserve a little bit of this or I want to make it my own? Or what did Roy Z tell you? What's the direction he gave you on this? Yeah, yeah. Well, he told me about, he just wanted me to be me. I guess. And I just did a, I sent him a bunch of stuff and I said to him kind of like, keep what you like and then replace what you don't like or what maybe I overstepped in somebody else's parts because he did not specify who was going to play what. I think he just wanted me to lay the foundation on the whole thing. And I did keep the original melody that it's even on the Maiden track. There's like this melody when the beat changes and stuff. And I did all that, that I kept as Maiden did it. And then I went off and I added my own parts.  And then Roy basically added leads over that kind of melody foundation. So, you know, there was no specific stuff. He just wanted me to just do a lot of stuff.  Well, I'm going to tell you, I like this version a lot better than me. Not to say I don't like the Maiden version, but I just like this one a lot better. And when I found out that you played on it, I go, makes sense. It's slower. The tempo is slower and the heavier. Yeah, yeah. So, yeah. And I think, yeah, that was the original way they had it. And then of course Maiden did it the Maiden way. So, yeah. It's a great track. The thing is a good song is a good song no matter how you can do many versions of it, you know? And if it's a good composition, that's all there is to it. Well, you know what? Congratulations, I'm really happy for you. You know, I think you deserve more of this stuff, like the epic stuff, right? Not to say what you're doing is not great. It's great. I'm just saying I love when you do kind of stuff like this. Okay. All right, on tour, Firewind's on tour in Europe, then going to North America. Everything is on firewind.gr, right? The website for all the dates and the tickets. The new album, Stand United is out now. It was released just a few days ago. Excellent album. I love it. Thank you. And congratulations on everything once again. And you know what? Enjoy your show tonight in France. What city? In France, Avonilla Temple. All right, guys. Have yourself a wonderful day. All right, thanks, Gus. Thank you, Jimmy. Have a good one.


Welcome back to our lecture series Math 3120, Transition to Advanced Mathematics for Students at Southern Utah University. As usual, I'll be your professor today, Dr. Andrew Misseldine. This video is the first video on lecture nine, and in this video, we want to talk about the idea of an index set. To describe an index set as, we have to first remind ourselves on this sigma notation that we probably have seen previously in maybe a place like calculus. We often see this notation where you see this capital sigma, there's some stuff on the bottom, there's some stuff on the top, and then there's a sequence of numbers right here. This Xi is going to represent the general formula of some sequence of numbers, and it's going to depend on some variable, which in this case, we've indicated that as i. That i, you also see here on the bottom, and represents the index of the sum. It's just a dummy variable that keeps track of which term in the sum are we in. You're going to see a number right here, which then tells you the initial term that is the first term of the sum, and then you see a number on the top, that's then going to tell you the terminal term, that is where does the sequence end. Now, these can be numbers, they can be variables like you see in here, it could be infinity for example. This in particular tells you where you start and where you stop, and then what is starting and stopping the number i, which you find in the formula right here. This sigma notation then represents an abbreviation of the sum, x1 plus x2 plus x3 plus x4 plus x5 all the way up to xn. And so this sigma symbol right here is then used to indicate you're taking this generalized sum. Now the Greek letter sigma here, you can think of as like the Greek alphabet, it's the third equivalent of a capital S. And a capital S here stands for sum. S is for sum here, and so sigma is just standing for a sum. It's a pneumonic device that when you see this sigma it's indicating to you're gonna add together some terms. Which terms? You're gonna add together these terms as they range from one to n like here. You see this all the time in calculus like when you talk about Riemann sums or power series, infinite series, things like that. Something that shows up less often in calculus is the counterpart of this notation when it comes to products. So if you see something like this, the notation looks exactly the same. You have a sequence of numbers, which we're calling xi. You have some index listed, we're also calling that i. And then this number tells you where you start the sequence. This number tells you where you end the sequence. And these boundaries could be themselves, specific numbers, variables, they could be infinite. The only thing that's different between this notation instead of a sigma, you now have a capital pi. Now we often think of the number 3.14, et cetera, when you think of pi, but this is a capital pi. And pi, the Greek letter pi in their alphabet is actually equivalent to the Roman letter P. It makes that puh puh sound. And so I want you to think of this capital pi as likewise a mnemonic device. Pi stands for product. And so unlike the sum, we're gonna combine together the end numbers because we have x1, x2, x3, x4 up to xn. With the sigma they're combined together using addition because it stood for sum. Now the product means we're gonna combine them together by multiplication, x1, x2, x3, x4, all the way up to xn. And it turns out that we're actually quite used to this idea of putting together products. We see them all the time, like for example, even if we haven't seen this pi notation before, we have probably seen things like in factorial. Now what is in factorial? In factorial is then the product of the number sequence i as i ranges from one to n. If you expand this product notation here, you would get one times two times three times four all the way up to times by n. And that's exactly what in factorial is. When you think of an exponent, for example, take for example, the number three to the fourth power. Or we'll even do just three to the n. This you could think of as the product of the constant number three as i ranges from one to n. This type of repeated products show up all the time just like we've seen repeated sums. Again, you just often don't see the notation. So I want to introduce that in this video. So we're used to that, oh, if you want to generalize an operation, you just use this big symbol, a big symbol to represent it. The numbers on the bottom tell you where you start. The numbers on top tell you where you end. This is the thing we're operating on. And here is the index of that situation. Now I should also mention that in order to make sense out of these things, we do need that our operations be associative. Associative here meaning that how you do parentheses does not matter. Notice that if you take x one plus x two plus x three, this is the same thing as x one plus x two plus x three. Addition and multiplication are binary operations. They're defined to take in two input and you make a sum or product from those two numbers. If you have an associative property which both addition and multiplication do, you can actually drop the parentheses and you can make it be any combination. You can add three, four, five, 12 terms together. It doesn't matter. There's no ambiguity whatsoever when you do that type of calculation. Now our goal in this video, in addition to reminding us about the previous notation, is actually to extend it to the setting of set theoretic operations. In particular, there's two operations we've played around with a lot in this lecture series already, the notion of intersections and unions. And so we can actually construct a generalized intersection and a generalized union. What does it mean to intersect three sets together, four sets together, five sets together, insets together? This generalization, because intersection is also associative, we don't need all of the parentheses, we can drop them down. And so to be in this intersection, a one, a two, a three, up to a n, what you're looking for is an element that belongs, it belongs to all, excuse me, it belongs to all of the sets in the collection there. And with regard to unions, how do you take a generalized union? How do you take the union of a one, a two, a three, a four? Well, again, we don't need the parentheses because the operation is associative here. If you take the generalized union here, you're looking for all those elements that belong, it belongs to at least one set in the collection. And these words, all and at least are things we're gonna talk about in the future. This is related to the notion of a quantifier that we're gonna talk about in the next lecture, not in this video, of course. So when you have a, you can take a large intersection of sets or a large union of sets because of the associative property, but it can get a little bit tiresome to write all the sets together. So what we can do is we can abbreviate the large union, mimicking the sigma notation we have before. So we're gonna take the union of sets that belong to our sequence, the AIs. And then the index represents the general term, the general token of these sets here. It'll range from one to N. Now, unlike addition where we use sigma as a mnemonic device and with multiplication, we use pi as a mnemonic device, there's so many operations under the sun that we can't come up with mnemonic devices for all of them. So oftentimes what you do is you just take the symbol for the operation and then you just gigantimax it. You just make it a bigger looking symbol.  And so this means that you're gonna iterate the union over the range one to N.  The big intersection means that you're gonna take an intersection of a collection of sets, I mean, where you range from one to N, like so. Let's do an example of such a thing. Here is our family of sets. We're just gonna do something simple while three sets right here. A1 is the set that contains the natural numbers zero, two and five. A2 contains the numbers one, one, two and five. And A3 contains the numbers two, five and seven. And so then if we wanna compute the intersection of the AIs as I ranges from one to three, this is just the abbreviation of the form A1, intersect A2, intersect A3. So we're looking for those numbers that belong to all of the sets in the family. Now, when you look at A1, zero is contained in A1, but not in any of the others. When you look at two, two belongs to A1, it belongs to A2, it belongs to A3, it belongs to all of them, so it makes it into the intersection. If you look at A5, excuse me, five is in A1, it's also in A2, it's also in A3, so sorry, that was a seven, there's the five. So five belongs there as well. So the intersection will contain two and five. But if you look at the other elements, one does not belong to every set, seven does not belong to every set. So the intersection will just be two and five, that pair right there. What about the union? Well, if you want to look at this right here, this is shorthand for the union of the sets AI as I ranges from one to three, in less compact form, this would look like A1, union A2, union A3. So we're looking for all the elements that belong to at least one of the sets. So you can go through each of the sets one by one. A1 has a zero, so does the union. It has a two, so does the union. It has a five, so does the union. Move on to A2, A2 has a one, so will the union. Two and five we've already considered. Then you come over to A3, two and five we've already considered, but seven we haven't, so we join it to the union. And so the union of these three sets will then be the five elements, one, zero, one, two, five, and seven. Those are all the elements that belong to at least one of the sets. Now it's also important to note that with the sigma notation we saw on calculus, it was often the case that we have like an infinity on top. We have an infinite sum, like with Riemann sums, the idea to find the area into the curve is to take an infinite sum where your rectangles get skinny, skinny, skinny, or with power series and the chlorine series and the like. When you have a series, you have an infinite sum. In that situation, the infinite sum is defined to be the limit of the partial sum. So we get something like sigma as i ranges from one to infinity and you have like an xi right here. By definition, this is the limit as n goes to infinity of the partial sum i equals one to n of the xi is like so. So that's how we define an infinite sum as the limit of partial sums. We can do the same thing for intersections and unions as well. So if you'd see something like this right here, we're gonna take the infinite intersection as i ranges from one to infinity of the collection of sets ai. This is then defined to be the limit as n goes to infinity of the partial intersection where we range only from one to n. And as n is allowed to get arbitrarily large, then we can take the limit, thus giving us this infinite intersection over here. We do the same thing for the union symbol as well. If you see an infinity on top, you should then read it as i take the union as i ranges from one to infinity of the ai's. This then means we take the limit as n goes to infinity of the partial unions. We're now i ranges from one to n. And thus we then let n get larger and larger and larger going towards infinity. And then the union is gonna be the set that's then derived by letting n get bigger and bigger and bigger and bigger. So let's look at an example of this as well. Let's look at this time at this family of sets of the following form.  A2 is gonna look like negative 202. A3 is gonna look like negative 303. And then if i is any positive integer, just for by way of notation here, we've seen the symbol like this before. It's the integers. The superscript plus just means we want the positive integers. So one, two, three, four, five, six, et cetera. So for any positive integer, we can define the set ai to be negative i, zero i. So for example, a5 is just the set negative five, zero and five. That's our formula right there. And so then we have this. Notice we now have an infinite family of sets because these sets are indexed by a positive integer. And so we then could ask ourselves, what is the intersection of this family as i ranges from one to infinity right here? Well, the ai's are just these sets right here, negative one, zero, it's not, sorry, not negative one, negative i, zero i. And so the intersection would then be what are the elements that belong to every single set of this form? Now when you look at just the first three, a1, a2, a3, the only thing that belongs to all of them is zero, right? Cause a1 has one and negative one, but a2 doesn't. a2 has negative two and two, but a3 doesn't. a3 has three and negative three, but a2 and a1 don't. They all have a zero. And in fact, when we look at the general formula, they all have a zero as well. And so when you take the intersection of this infinite family, the only thing that will belong to all of the infinitely many sets will be the number zero. So the intersection is just this singleton. Conversely, they'll look at the union here. If we want to take the union as i ranges from one to infinity of the family of sets, a i, this is the same family of sets, negative one, zero, sorry, negative i, zero and i there. We then want to take the union. So if you belong to at least one of the sets, you belong to the union. When you look at the a1, you're gonna get zero, negative one, one. When you then unite with two, well, you're gonna still have zero, that was already there. You got two and negative two. When you unite with a three, again, zero is already there, but now you gain three and negative three. So then if you were to unite with a four, you're gonna gain plus or minus four. When you unite with a five, you're gonna get plus or minus five. When you unite with a six, you're gonna get plus or minus six. And in general, when you unite with a i, you're gonna gain the elements plus or minus i. So you get both the positive and the negative integer there. And so then we can see that this union is equal to the set of integers. Every integer is represented somewhere. If you take some integer z, then n is going to then belong to the set A, absolute value of n, because n could be a negative number, right? It'll be inside of there. You get this negative n, zero, n in that situation. I guess the only potential issue would be if n is zero, but zero belongs to each and every one of these sets. So that's fine too. So the union of all of these sets does turn out to be the integers. This was an infinite union and an infinite intersection. Now we've talked a lot about unions and intersections. I should mention also that this notation applies for Cartesian products as well. Now a Cartesian product, we think of actually as multiplication of the sets. And so the symbol we use, instead of like a giant x, you actually use the product symbol that we introduced before, the capital pi. So when you look at this notation right here, this means we're gonna take the product of the sets, A i as i ranges from one to n in that situation. Well, if you're taking a product of sets, this is gonna be the Cartesian product. So this by definition is then the Cartesian product, A 1 cross A 2 cross A 3 cross A 4, all the way up to A n. Now we've talked a lot about the Cartesian product of two sets. This is by definition the set of all ordered pairs where your first coordinate comes from the set A and your second coordinate comes from the set B. So we write that as something like the following. But we can generalize the notion of a Cartesian product to then if you take the, if you take a Cartesian product with n mini sets, you then take the set of all list of length n. And remember as we introduced list in the beforehand, a list by definition is ordered. So you don't have to call it an ordered list, all lists are ordered. And so the first element of the list is taken from the first set. The second element of the list is then taken from the second set in the product there. All the way down to the nth term of the list comes from the nth set right there. That's what we describe generally right here. AI comes from capital AI. And so this is the set of all possible in length list where elements in the list are taken from the respective sets right there. Thus generalizing this ordered pair of bits as we had seen before. Now this product, we can have arbitrary Cartesian products but one that's extremely important is when you take a set cross itself, cross itself, cross itself and you do this like say n times. Now like we talked about before, Cartesian product we're thinking as a multiplication of sets. And so what you can then do is you can define that if you take the in fold Cartesian product of a set with itself, we then call this the Cartesian exponent. And we use exponential notation here. A to the n means the Cartesian product of a n times. And so then what does a typical element here look like? I guess I should write this the other way around. Nope, I was right the first time. A typical element here would be a one, a two, all the way up to a n. So the set a n is then just in length list of elements coming from a. And this is something we actually see a lot like in geometry, maybe calculus or algebra if you're doing some analytic geometry. In linear algebra, you see these types of notation used all the time. So for example, the set R2 is by definition the Cartesian product of R with R. And so this would then be the real plane where the elements of the real plane look like ordered pairs X, Y. Those are the coordinates we give. Like in linear algebra or multivariable calculus setting, you might also have seen R3. This by definition is R cross R cross R. And this gives us three space where elements in three space look like ordered triplets. An ordered triplet is just a list of length three, of course. And so this is notation we've seen before and we will be expecting to see things like this, of course, in the future. Now, before we end this video on index sets, I do want to then describe why do we call them index sets? It turns out all of the sets we've been considering with these unions and products and intersections, your index always turns out to be a natural number. It turns out that is not required. There are times where it is inconvenient to index a family of sets using natural numbers. And there's also times where it's impossible to use the natural numbers to index a family of sets. And so the titular topic of this video here, the index set is exactly that. If you take a set I, we call it the index set. If the elements of that set are used as tokens, markers for sets in some family, okay? So consider you have this family of sets, A sub I. Well, that I we put as a subscript there, it's just a marker, right? It just tells you like this is the identification number for that set. And then the index set I is just then the collection of all of the identification numbers that are possible. And this set could be a set of natural numbers. It could be something much, much, much, much bigger than the natural numbers though. And so if you then talk about the intersection of a family of sets indexed by the set I, we write things a little bit different. Instead of having something on the bottom and something on the top, we actually just put it all on the bottom right now. And so then when your top is blank, you should be thinking of, oh, the index set is on the bottom. For which this right here is still our index. This is a generic arbitrary marker. This right here though is the index set. This is the set of all possible markers you could use to describe the sets right here. You still see a big intersection symbol, which means we're gonna intersect something. What are we gonna intersect? This family of sets right here, where again that I is used to indicate the typical element, the typical marker of this set. And so by definition, this intersection is then all of the elements that belong to all of the sets here. And this is the keyword here, all. The intersection grabs those elements that belong to all of the AIs. Now, conversely, if you use a big union, you then see the index set here on the bottom. So this means we're gonna take the union of sets of the form AI, where AI is indexed by the set capital I itself. And this by definition is gonna be all of the elements X, which belong to at least one of the AIs. And that's this keyword here as well, at least. At least one describes unions, all describes intersections. And we will see this in the next lecture, this idea about quantifiers. For all is one of these quantifiers, the so-called universal quantifier. And then the other one is the existential quantifier for at least one. We'll make some more sense out of those next time. Now, what I wanna then do is then consider an example of a infinite union and intersection where our index set is something other than the natural numbers. Because when we looked at those intersections and unions before with the infinity on the top, you took like I equals zero to infinity AI. I want to make mention that using the notation we just introduced, this should just be like, oh, I belongs to the set of natural numbers of the AIs. So ranging from zero to infinity just means you're just ranging over, your index set is just the natural numbers. Or if you range from one to infinity, you're just ranging over the positive integers. So those are just special cases of what we're considering now. Now, in this example right here, what we're gonna do is we're gonna take our index set to be the interval of real numbers between zero and two, inclusive, so zero and two are both inside that. This is not an interval, there's not a set of, it is an interval. It's not a set of natural numbers. It only contains three natural numbers, zero, one and two. There are a lot of real numbers in there, both irrational and rational. Now, using this index set, we're gonna describe a family of sets. We're gonna call them AI, and AI is gonna be abbreviation for rectangles. Remember, a rectangle is just an interval, cross an interval, and we can view this as a subset of R2. Now, the first interval is gonna be the interval I to two, where I and two are the X coordinates here. I, of course, is the index of the set. And then the second interval will be zero to I, where this is now describing the Y coordinates. Again, I is the index of our set. So this is gonna be a rectangle whose vertices are I zero, two zero, two I, and I I, which I have an example of one illustrated here to the right. So if this is the rectangle associated to index I, it'll contain as a vertex I zero, two zero, two I, and I I that you see illustrated here on the screen. And now as I ranges between zero and two, you can get lots of different rectangles. Here's such a rectangle, another one would look something like this. And so you get these different rectangles based upon your index I. So then what I wanna consider is what would be the intersection as I ranges on the set zero to two of all of these AIs. All right, can we compute this thing? Now, I wanna make mention that this intersection is going to be a subset of any individual set in there because if you belong to the intersection, you belong to all of the sets. In particular, you belong to a particular set. And so if you look at A zero, pause the video to compute this if you have to, but convince yourself A zero is just the interval zero to two along the x-axis. And likewise, I wanna mention that, let me write it this way. If you consider the set A one, this would be the interval, I'm sorry, A two. This would be the interval because A one would be this rectangle right here. A two would actually be this line segment that's vertical right there. If you look at these ones, what do these two sets have in common? The only thing they have is this point's two comma zero. Now, two comma zero belongs to both of these sets. If it belongs to the intersection, it would have to belong to each and every one of those. And you can convince yourself that two zero does in fact belong to each and every one of these rectangles. And because of the two sets we just consider, that's the only thing that belongs to everything. So the intersection will just be the single 10, two zero in the plane. Now, let's go the other direction. Let's take the union now of these sets as I ranges from zero to two in the interval. Take the union of all of the AIs. So what we're gonna do is we're gonna take every point in this rectangle. We're gonna take every point in this rectangle. We're gonna take every point in say this rectangle right here and we allow these rectangles to vary. Now you might notice on the screen here, I have this triangle drawn like so. Whoops, try that again. Call this triangle T. I claim that the union of all of the AIs is actually equal to the triangle T itself. Now clearly by construction, each of these AIs is gonna sit inside of the triangle. So that gives us inequality in one direction. But for the other direction, I want you to note here that if I take any element inside of the triangle, call its coordinates X comma Y, I can then draw a rectangle that contains that point. In particular, I can take a rectangle where that point is actually on the line segment on the top of it. And so every point of the triangle belongs to at least one of the rectangles and therefore belongs to the union. This then shows us that the union of all of these rectangles is in fact equal to a triangle. And so this is a really fun example to end on here that it shows us how infinite unions and infinite intersections can be indexed by anything. Doesn't have to be natural numbers and how one can actually calculate these things. Notice here when we talked about this, I made an argument that containment went in one direction and then a different argument that containment went in the other direction. If two sets are subsets of each other, that actually makes them equal to each other. This is a proof template we saw beforehand. But isn't this a calculation? Didn't I calculate this set? I wanna point out here that it turns out proofs and calculations are really the same thing in mathematics because all they are is just mathematically correct communication that expresses mathematical truth.


Ooh, these bingles receivers talking spicy. Yeah, this feels like a dream. So YouTube team keep it clean. What's going on? It's Engraven here with another video. And in this video, the big three, the trio of NFL wide receivers that set the world on fire last year and made it all the way to the Super Bowl. And then we know what happened then. But still, they made it and nobody else did. And they were a huge, a huge part of all of the bingles success. Jamar Chase, T Higgins, and Tyler Boyd, they were on the pivot. And shout out to the pivot, by the way. I love what they do over there. Shout out to Ryan Clark and Channing and Fred T. Anyway, they were on the pivot and they had some very interesting things to say. And you know what? Just roll the clip. Oh, y'all sit on the sideline, y'all bombing on people. You like it. It's actually easy. Not a word, yeah. All the time. It's not Raven's game. Raven's game, Chief's game. All the time. We on the sideline, they can't double all of us. Somebody got to go off. So that's how we look at it, you know what I'm saying? If they double, you know, one or two of us, next person man up. As you know, it's always more out there. So that's how we go. So Ryan Clark, a former Pittsburgh stealer, by the way, who has been doing an excellent job as an analyst and on-air talent? He is phenomenal at what he does. And I was so glad that Channing and Fred, that they linked up with him to do the pivot. But anyway, Ryan Clark, he had them on his podcast, his platform, his channel, his everything with the pivot. And he was asking the question. So do y'all ever just sit there and just feel like, man, like this is easy. We all bombing them and whatnot. And T. Higgins was like, yeah, we do. And then Tyler Boyd, they brought up the Ravens game. And Jamal Chase was like, yeah, Ravens game. And then they brought up the Chiefs game too. And where they went off, and they did. They did. And now I know most people, or at least most Ravens fans are thinking, man, like, hey, context is important because it is. It is extremely important because we know in that second Ravens game, that was 525 borough, where I said that, hey, I gotta call him 500 borough from now on until the Ravens actually stop him because he went off. And the receivers, they went off. And you know what, let's just look at, I know we don't wanna revisit it, but let's just look at the numbers. T. Higgins, he had 12 catches for 194 yards. 12 catches for 194 yards and two touchdowns. Jamal Chase had seven catches for 125 yards. Tyler Boyd had three catches for 85 yards and a touchdown. So all three of them, the big three, they went off through the air. Now, who are they going up against? Yeah, let's not know Mark Humphrey. Let's not know Marcus Peters. It was not no Anthony Averett. You know, honestly, I don't even remember half the corners that we had out there. That might've been Robert Jackson. I think maybe Keevon Seymour, maybe Worley was out there. I don't even remember half the guys that was out there because so many of Raven's players were injured. They were injured, they were hurt. Ravens ain't had starters out there. They were playing with the backups, backups, backups, not even the backups, not even the backups, but the backups, backups, backups. It was rough. It was so rough. But the Bengals, they don't care about that. And nor should they.  That's all you can do. The Ravens were in the same situation. They just gotta play the team that's in front of them. Whether the other team got all their starters or not, you got to do what you got to do. But then, this is where it gets very, very interesting. Knowing that the team didn't have the starters and you still talking spicy like this, ooh. That's the kicker right there. But I love it because reason being, if they whooped you, they threw for 525 yards. They caught 525 receiving yards on your defense when everybody was not healthy. All right, cool. No problem, they did it. Now, show them what they won't do when you are healthy. That's it. That's all you gotta do. Show them what they won't do.  And when they did have a little more health in a secondary. And that game, Jamar Chase, because he had Marlon Humphrey spinning around his, oh, Marlon, you okay, man? I felt so bad. It was rough. It was rough. It was a rough game. But anyway, Jamar Chase in the first game where Ravens had a little more health, Jamar Chase, he had eight catches for 201 yards in a touchdown. That's the game where just nobody wanted to tackle. No, nobody wanted to tackle. CJ Uzama, he had three catches for 91 yards and two touchdowns. I remember one of them, he was just wide open. Wide open, I'm looking around like what? And then there was another one where he ran over somebody on his way to the end zone. Yeah, T Higgins in that game. He had seven catches for 62 yards. Tyler Boyd in that game had four catches for 39 yards. So you see, more starters played in that game. But the Ravens, so the most starters played in that game for the Ravens, I mean, excuse me. And the Bink, well, besides Jamar Chase, I mean, they still got this. They still got this.  I mean, they over here, oh, but yeah, we remember Ravens and Jesus. Okay, yeah, they should remember that because those games, especially against the Ravens, that's where a chunk of their yards for the entire season came from. They could have probably made the Pro Bowl based on all those games alone. And they did speak facts in there too. When they said, all right, you can't double all of us. Who you gonna double? Because if you double this guy or you double these two guys, then this other guy could go off. You decide you want to bracket coverage him or you want to bracket, okay, well, we still got him. And that is such a beautiful formula. And on the flip side, that's what I'm hoping the Ravens end up doing and the Ravens end up having. And just to sort of change the direction of this conversation, that has been one of the biggest reasons that I've wanted the Ravens to really go in at the receiver position because you can never have enough playmakers. You can never have enough talent. You can never, because it makes your quarterback's job that much easier. Look at Joe Burrow. Look at Joe Burrow, they had like, Ravens offensive line was bad, ooh, they were bad.  Think about, like think about that because we, as Ravens said, we know how bad the Ravens offensive line was last year. It was terrible, but the Bingo's was even worse. And they made it all the way to the Super Bowl with that terrible offensive line. And they were a play away, a play away from being successful in the Super Bowl with that bad offensive line. But what was the big reason for that? The wide receivers making Joe Burrow's job so much easier. He could throw a slam. He could throw like a eight-yard slanted Jamal Chase. And I mean, we, as Ravens fans, we saw it firsthand, especially in that first game. There was like, I think it was actually an eight-yard slanted Jamal Chase. Marlon Humphrey go to tackle Ole Miss. Somebody else go to tackle Ole Miss. Boom, end up being, what, 50, 60-yard touchdown? Just like that. All Joe Burrow had to do was throw an eight-yard slant. That's all he had to do. But since he has elite talent at the wide receiver position, that made his job that much easier. That much easier. That was another play. It was in the second game because where T. Higgins was going off. There were some times where Joe Burrow just threw it up. It looked like he was just having fun out there. He just threw it up, threw it up.   Let me get on these steps, caught the ball, and okay, I'll come back down there. He's just a monster, dude. But when you have that elite talent, it makes your job easier as a quarterback. So again, that is one of the reasons in the examples of why that's why I wanted the Ravens to do the same thing for Lamar Jax. But anyway, back to the original. What were you originally talking about? It's up to Ravens' defense. First to get healthy and stay healthy, first and foremost.   It's all about that action. It's all about that action. So the Ravens will have at least two times this year to show like, hey, what happened last season? Yeah, great job, it was cool and all, but y'all gonna know what's up this year. Yeah, this feels like a dream. No jazz, but I mean. What I mean. You too, T, keep it clean. You see my boy, he like got him made it. Got him made it. Boy, that's my homie, ain't that right in Ravens? Right in Ravens. Shout out to Ravens.


Hey guys, welcome to Higan Irruthil and we're here and we're doing a account showcase Versus free-to-play and a paid account. So both accounts are mine The paid account just wanna have a disclaimer. It used to be a free-to-play account It it was it's actually my vanguard server account for launch when global launch came in I decided to Invest a little bit on that one while this one is my Asia-Pacific account so This one is purely free-to-play and I just want to show With you guys what my progress is so currently I'm at 60 This is I think as of today's April 11 if I'm not mistaken So I'm at 60 my progress is actually doing good. I don't have any You know, I'm not stuck anywhere. So as proof I haven't bought the Fenn Beginner bundle here. This is purely free-to-play. Let's take a look at my roster here guys and So far I'm focusing on a few Heroes, I'm not really spending much Uh in terms of resources in with a lot. I just got eluya by the way. So Again, uh, and I decided not to invest in screamer at this point I decided to go with roco because I want to compare long-term roco and Nuno which is in my Um, vanguard account, which is paid account. So again, this is what I have my main team here I don't have much I tell you my this is what I really really have so six Six ssr's and a lot of sr sr. So my main team is gildan media Rita And roco that is my very main team in going over content PVP pve Sometimes I use fin but recently I haven't because I've been using rita's rita. I got As an off banner pull fin I got her in the select ssr. If I'm not mistaken live is also an off banner pull eluya I got from the pity on her banner. So and gildan is also No, no, I forgot because I I think I got gildan in I think in her banner if I'm not mistaken, but the only off banner here is live And rita the rest are in their banner. So this is my account. I don't have a problem with this account. Um, again It's it just lacks Heroes, but again, it runs smoothly. It runs in clear stages It's again, it's it's a bit delayed because this is an asia pacific account And this is a global launch account. I just want to share with you guys If you want to add me as your friend In the asia pacific account of yours if you have an asia pacific account, you may add me here so Um friend requests Like why I can I'm sorry. Um, here it is the add friend Okay, so you may add me. This is my user id 4728 8 7 900 8 8 2 5 You may actually Add me just type in this number. You may pause this video and add me as your friend This is actually based on the asia pacific Uh server. So this is my global launch account officially So this is how free to play looks while we move to the paid account So this is my vanguard server account. This is a paid account Uh, approximately, um, just want to go through the shop I did spend for the monthly card for this one So this is five The bundle I I bought this one. This is two. So that's seven then For the limited no, I didn't get anything. Um, the top up I did one. I did one here. So that's roughly eight and the fan, um The fan deal, which is one dollar or point 99 cents I got that one as well. So that's a total of nine. So that's under 10 and I don't think it has a lot of difference Um, just gave me a lot, you know, in this this account is actually way ahead anyway And it gave me more of a boost moving forward because I'm actually More concentrating on this because long term. I'll be playing this more Um, I just wanted to gauge whether free to play and global Can really, you know, catch up with what I have with what I played in soft launch and with the vanguard server So Again, this account here so far for the wish I have saved a lot I won't be pulling for no no because I have no no I won't be pulling for For rita because I have rita. I'm saving up for the next new banner that will come out I'll probably just pull for this one. But I already have lubellia for no no So I might as well skip that as well So for my roster if you can see It's a bit advanced The the other one the global one has six ssr. This one Has nine So the only difference is siacom no, no sir slip The rest are in my in my Free to play account. So live eluya rita fan media and gildan are there The only additions here is sir slit. No, no and siacom siacom I used to use Him when I was starting in soft launch. But again, this is my lineup and plus I have roco here as my initial healer I cannot I can no longer reset because We played in vanguard. We are playing vanguard. So we're already past the two week reset And screamer here as well. I cannot reset. So that is why I'm building screamer now As part of my team. I just want to you know develop this account. I'm probably There's a lot of things I cannot no longer reset here So again, um, just have to be contented with what I have and what I've invested in and so far This is it. So this is how it looks in terms of not really a big difference if you can say My main team right now that I'm using is gildan No, no sir slit gildan rita Rita because the buff goes to sir slit by the way And um, either I'm using roco or screamer for the healer. So I'm experimenting now with screamer So mostly this is an all fire team With gildan not really all fire team.  So I don't have I can actually do a all fire team with arman That will take a lot of investment If I get probably more copies of arman, I'm inclined to use her I used her actually in the soft in the in the soft launch. I had a way way You know the free to play account The global account was way better that the when he started than this one. This was way worse when he started I didn't have I didn't have gildan. I had arman for my guardian. I had media I had fen. I think that is it The rest I got for off banner pull siacum was off banner live was off banner Eluya I got in the banner is pity. No, no is pity as well Sir slit recently, but when I started I only started with arman roco media and fen That was my starting unit in the soft launch. So again, this account has come a long way And again, there's only a little investment here. It isn't really it hasn't really made a dent in terms of You know per se terms of anyways, it's just nine So again, it's not that much. You can't see it now, especially for the monthly pack But again, this is this is both of my accounts. So I'm playing this every day. Also guys, this is for vanguard For those who are in vanguard server, you might also want to add me as a friend So this is my user ID for vanguard Please make sure that you either add me in asia-pacific and for the previous one And this one is for vanguard server. So for seven three seven four three eight nine three seven eight six zero So that is it. Just add me here. Then I will accept you guys. I haven't added Friends yet, but definitely if you want to request Then I will accept So there you go guys. Those are my two accounts. So what do you think of my two accounts? I'm playing this every day both of them And um, I'm actually contented with both of them. I have time to play both of them actually So That is it. Um comment down below what you think of both my accounts vanguard and asia-pacific accounts What do you think of them? Are they okay? Are they not good? I think you guys have a better account than what I have But I'm already happy with this This is livable already I just need a couple like for example my wish list Is uh, what my wish list is Caesar. That's it If I get Caesar Then I'm good. I don't even have gear at this point So if I get Caesar and motess jew, I'm already happy with this account. So Caesar Um another you know garden that I'd like to experiment on team building But unfortunately, I don't have at this point Motess jew in one of my re-rolls. I got her But I opted not to use that that re-roll. So Again, that is it Hopefully again Comment down below guys. Uh, I want to hear from you. Thank you very much for staying this far. Take care. Stay safe This is the warden and I'm out of here


At the end of the last video, I said I was going to record another one right after it and I'm recording this episode right after the last one. Hello people of the internet, my name is Johnny and with no time to waste, welcome back to FNAF World Edgertime, we're fighting Twisted Bonnie, I guess. You know, I always did find it weird why Funko made this pop figure blue, even though Twisted Bonnie is very clearly purple, even in the original teaser. Twisted Bonnie is purple, so why his pop figure is blue? I don't know, why am I talking about this? I don't know, let's see what's going on. Holy, what the heck is that thing?  This nightmare you won't wake up from. For failures, we've all been gathered, pressed, amalgamated into dark Twisted Demons of your friends. The needles sharpen, every step we take, the pain never stops.  The only thing I want to hear, why did it get so much more quieter? What the heck? The only thing I want to hear is Mal hair, is where Mal hair is. Ignorant child, I will not let you find him, I will not let you walk out of here until you are broken into pieces.  Still sick, boys. Oh, interesting, interesting. Okay, so we're fighting this guy now, and he looks like he is going to be a big hard fight, is what I was going to say. I don't know what you guys would think, Jesus.  Yeah, notably, hi, Cord.  What, did it skip Ferdy? I think it skipped Ferdy, Jesus.  Because it can like, it basically is a one hit, and that's just so insane. Anyways, yeah, nearly half the way there. Yeah, don't really know what to say, I'll be honest. I'm always confused on whether or not I should leave these fights in or not, because yeah, you know, it's cool and it's entertaining, but it basically is the same thing over and over again. You know, it's just, this is a different sprite from the other fights, a slightly different background as well. The only thing that's really different is, is those two things, you know, we're using the same characters, we're doing the exact same attacks, so I never know whether or not I should leave these fights in. I do anyways, mostly because I usually talk over them, for example, right now.  Sorry, I thought we were about to game over right there. Oh, of course, my favorite. Oh, come on.  Who's doing a thing right now? Thank you. So yeah, there's that. Yeah, if there were different characters and there were different moves we could do, I would definitely leave in a lot more fights, but I don't know, normally I just talk over them anyway, so I just leave them in, so yeah, there's that. Anyways, we finished that fight, managed to talk my way through it, as usual. Wanda, beyond those thin lines, under the dome keeping secrets in disguises, boxes, what? Will you suffocate or be guided into the light? Ah, why do they keep doing that? It's always so bright on my eyeballs. You're just speaking loads of gibberish, poetic gibberish. Yeah, I know it's gibberish.  I said it wrong and I decided to stick with the bit, or perhaps a clue. Well, I wouldn't say it was a clue, it was more of just straight up directions. Alright, so follow the thin lines, and I think he talked about the dome, which, if I'm correct, is up here. This is the dome, so follow high, follow the thin lines. Honestly, I nearly just walked into this guy without even seeing him. I found Twisted Foxy.  You, come forward. Do you feel it? Do you feel it? Your sins crawl up your spine, dig through the moulds of your body. They hunt for what lies within to shatter you from the outside.   Idiot, you do not comprehend, therefore I must make you. What? Oh. Well, I like the Twisted characters so far, they have some fun dialogue. Oh, and we're going straight into Under the Fight.  These guys, I always like to, um, ah, nope, that's not what I wanted.  So far, not that bad. He really doesn't seem that bad. His attacks, I don't know, I feel like he's a bit easier than Twisted Bonnie. Then again, he hasn't really attacked us just yet, so I guess I can't really base this fight just yet. Oh, oh, um, well, that definitely, you know, changes things. Ah, that really does change things. Yeah. Oh, please stop. God, Gigabyte is the freaking worst. Um, yeah, halfway there. Not too bad, okay, pretty bad right now. Freddy does not have a gift box, and he is basically our main healer. Oh, great, great, great, great. You see, I will say, going back to, you know, having different characters and all that in the game, I will say that once you play the game, you realize that there's just a pattern to everything. Like, you know, Freddy, I always have him healing. You know, he always does, I don't even know what it's called, quick repair. Candy, grid turret, and then the wall. And if those things are all set, then you just wall up. Um, Wendy, I always do bone. I don't know which one of the three of her attacks is the best, but I always just do bone because I know where it is. And then Belora, you know, med beacon, and if that's all set, then you do counterpart. And if both of those are all set, then you do her third attack. It's just a repeating pattern. Just don't really know where I was going with that, but I just put it out there. Alright, level 21. Nice. Now we got a few rewards for it as well. So, Foxy, what do you have to say for yourself after your horrible defeat? Again, they always just say, within the deep forest, the spirits hunger, starved and unknowing. Will they swallow you whole or guide you to the light?  Coincidence? I think not. This is so weird. Yeah, it is very weird. And I could have gone my twisted Foxy pop, but I didn't. Let's see, who is next? So, in the woods, that's not the woods. This is the woods. Yeah, let's just, hi. Let's just go to the start of it, and then let's check every single possible location. Hey, gee, he's twisted Chica. Oh my god. You don't look anything like twisted Chica, though I will say. The twisted characters in this game are by far my favorite. They just look so goddamn good. Freddie? Freddie, is that you? What the heck, how do you have that voice? Please help, it's so dark, so cold. No, you're not real, you're not actually Chica. It hurts so bad, I'm so hungry, I'm so hungry. I'm so hungry. Jesus Christ, what is going on? Was that Chica? Who was in there? And why are you talking to me like you know me? Maybe you do know me, maybe it's part of the law.  Alright, this fight I'll probably, oh, I'll just fail you guys in when something interesting happens.  Oh my god. I want to know why they can do that, because some of my guys still have gift boxes.  But I did say we were gonna die, so I guess we had it coming.  Alright, level 22. Level 23, nope, level 22. Man, if we like don't get enough rewards for those fights, like that was pretty tough, not gonna lie. They got like one gem from it. Alright, what are you gonna say? Good, bad, who's so bad? The greatest gem of the beast.  It sounds like you're chopping down a tree. Lives within the oars of sorrow. Yeah. Why do they do that?  Yeah, pretty alright. No, not really. Why? They look like my friends, your gang, which means, yeah, which means what? Pretty, I don't know. Found up. Ah, I was expecting this, but I still wasn't prepared. Oh my god.  Oh my god. So, what are you, besides a cheap knock-off? I am the purest form, the greatest creation. What you should have been. Wait, is that? These clocks you shall not reach.  These clocks you seek, cheat. These clocks you seek shall not reach your filthy hands. Wow. I will make sure of that. Okay, now the fight, here we go. Alright. Deadlights. I didn't know I was playing it, the video game. I think the deadlights just knock out my wall immediately, which is not really that good, because that wall protects me from his attacks. Then again, he really hasn't done anything other than deadlights, so maybe he doesn't have any other attacks. I don't fully know. He is halfway there, so this fight hasn't been too bad. But yeah, as the final twisted character we fight, he has not been bad at all. He's probably been the easiest one, which again is weird since he's the final guy, you know? Yeah, this guy was so easy. What the heck? How was he the final twisted guy we had to fight? And if he's giving us the clock, then that was like the easiest fight to get a clock I've ever done. What the heck? Alright. I think we do have enough to get the final boss straight as well, but we have to double check. Oh, he's not even here. Well, we got three clocks and probably a lot of nightmares. So what do we do now? We shall return to consequences. Yeah, that's probably the safest bet. Alright, well, let's do just that. So we have three out of the five clocks, which is very nice. We nearly at the end. Probably. Hopefully. Ah, just in time. Just in time for what? You've gathered three clocks. Yes, sure did. Well, I managed to get my hands on the fourth. Oh, my God. We are going to be close to that end. What? How did you get a clock? How did he get a clock? That leaves just one more, and I have a suspicion of where it could be. Well, hey, we're this close now. Spill the beans, man. Spill the bean, consequences. The palace holds many secrets. Perhaps lurking somewhere in the palace is the final clock. Got it. We got no time to lose. Let's do it. Good luck, Fazbear. Good luck to you all. I want to know how consequences got that fourth clock. Oh, well. Dreadbear, what's up, man? Oh, with scrap baby as well. Ah, I've been expecting you for. Dreadbear, my man was the last clock. Why? Right here. Is Elizabeth the last clock? Is that what you're trying to tell me? Dear Elizabeth here has been holding on to this one for a while now. Elizabeth, sweetheart. Look at me. Oh, no, music right here. Please. Your heart was always so pure, so full of love and care. I'm asking, no, I'm begging you. Come back to me. To us. Ah. Dreadbear. So she won't be doing any such things. Now, we have business to attend to. Toodles. Why do they do that? Shoot, they're getting away.  A ward without you is a better one already. Eight of your failures will now show. Now feel our pain. Huh. Well, Grim Foxy's here. And he only has one M in his name, which means that this is not the official Grim Foxy because Grim Foxy actually has two M's in his name for some reason. I think this is the official model. Like in all seriousness, this looks like the official model of Grim Foxy, which I wouldn't be surprised if it was. I love, I absolutely love it when games put in official models from FNAF VR. I just, I don't know. There's something about seeing those official models in fan games that just, I don't know what it is. I don't know. But I also do love when people make their own models, like all these adventure scrap characters and all the twisted characters and adventure Dreadbear and adventure Glitchtrap. I love those.  Long story short, I'm just saying that I do love this game, right? Even though I get, you know, a little irritated here and there, I do really enjoy this game. And the fact that this was, um, it was like canceled and now the creator's not working on it anymore and it's still this good, that's a major plus. And Grim Foxy is almost dead. Not really that bad, I'll be honest. Not really that bad. Alright, yeah, he's nearly dead. I don't know if this is going to be the final episode. It feels like we're getting closer to the end. Oh wow, that's a lot of ones that I just took damage for. Wow. Alright. Level 24, we might be getting closer to the end. It's all because of consequences. He got a clock without us and now we're like super close to the end for some reason. Pretty. Hmm. You look tired. I mean, we're all kind of tired. It wasn't your fault. Once we get the clocks, everything will be okay. Right, right, we don't even have the clocks. I just forgot about that. Grim Foxy was not, we weren't even fighting him to get the clock. Alright, I guess we're going up here then. Oh, what's this place? The Astral Valley. Oh! There was an Astral Valley in the first game. Actually, what I want to do quickly, before we hop in all willy nilly, I want to quickly find out can we get, yes, that should be everything in the shop then. Oh. 20 and 10. Alright, that's going to take a long time, but other than that, 5, that's going to be helpful. That's going to be really helpful. Alright, I think we should be good. Alright, let's hop back into level number 10 and let's see what is going on. Oh, hey, red band and white rabbit. They were in the original FNAF order and now they're back for the edge of time. Alright, ooh. So we just like straight up confront Elizabeth, right? I guess so. Here we go. Elizabeth. Stop. Stop calling me that. I am baby.  I'm simply just baby. This filth wretched ward, it will know how badly it hurts us. That's not you speaking, but I know you're in there. Please. I'm sorry, but this was never my choice. So are we fighting Elizabeth right now? Yes it is and she has helpers. Oh my God, this is going... Are you kidding? This is going to be the worst fight ever. This is going to suck. Oh my God. Well, I will tune in with you guys once I'm dead. Oh, right. Paloa doesn't even have any gift boxes anymore. Yup, I'll see you guys when I'm dead. Right?  Also, I couldn't put up my wall for some reason, I think. God, this is just the worst. I am going to... Oh, we got rid of one. Oh, we got rid of two. We got rid of three. Oh, that's going to suck. Ah, damn it.   Thank you. Yup, nope. Damn. I think we're going to... We're going to need that... What? What?  We're going to need that final gift box. Yeah. I don't know, I guess we'll just keep trying it. Yeah, I don't really know what else I can do. I don't know how to get gems. I think I can only get them from bosses, but I don't have any other bosses to fight.  Oh my god. Hey, I finally got some gems and it's only... Total of six. Three each. Which gets me nowhere close to getting the final power up. That was... I hated that so much. That was the worst thing ever. See, it doesn't come... Oh, well, okay. Here we go. Oh, she turned into baby. I mean, she turned into blower, I guess. Blower. It'll be okay. We have all the clocks now. Let's get this back to... Not so fast. Huh, none of you. Show me. Uh, Bobo. What? No one calls me that anymore. How do you like this little game so far? Fun, right? Watching as my viruses tortured you was just wonderful. But now everything is in motion. Yeah, yeah, yeah. Here to ruin everything. Sorry. He took the clock. Oh my god, I spent all that time getting that clock.  What? I think it is. I think it might be. What is it going on? I feel like I'm just going in circles. Okay. So you go here, here, here. Then you go up, and then to the left, to here. Then you go back in. Then you go down, then up, and then you go down to, um, I think it's down here. Yeah, it's down here, to here. Then you go, yes, okay, found it. Sure. God, I'm just happy I made it through. Oh. It's like the Foxy minigame from the original FNAF world. I really like the drawing in the background. Man, this is bringing back some good memories.  The one that's like, listen to my voice, and you will find the key. Uh, that was a good minigame. When you can see how fast can you flee. It was a good game, good game. Um, I don't remember who voiced Foxy in that, uh, or withered fox, I should say, in that minigame. Though I don't know if they ever returned. Oh, wait. Oh. Oh, oh no. Oh, gamers, bad gamers. Oh. Oh, I really don't like how you jump with shift. I'll tell you that, boys. Yeah, I'm just gonna keep jumping. Yeah, I'm just gonna keep jumping. Can I hold down? Oh, I can hold down. All right. Yeah, I'm just gonna hold down everything. Oops. Maybe I shouldn't. I don't know. I am fighting Dreadbear though. So this is very interesting. All right. I wanna watch out for that thing, cause that comes by fast. Oh, watch out for these.  All right, watch out for the missile. Yep, yeah. I don't think we're gonna make it this one. I'll tell you that. Crap. I just jump into them. Ah, God. Yeah, I really hate jumping with shift. I'll tell you that. Hey, I did it, I think. Oh! Oh, yes, of course. Oh, no. All right, so I don't need the mouse for this. Um... I don't really know what's going on. But I'm gonna go with it. Oh! All right, so he still does fire attacks. Ooh. Oh, God. He's kind of tough. I mean, that attack right there, ooh. That's not my... That's not the threat. That's the threat. All right, so we don't really wanna get too close to him. Okay, we also wanna dodge his... Ooh. We still wanna dodge his attacks though. Ah. Ooh, nice. Nice blow up.  Ooh, he's switching it up a bit. Ah, I just ran right into those. I didn't even try to move out of the way. Oh, my God. I moved so slow. Here we go. Ooh, there we go. There we go. Don't get hit by that though. Ooh, go down. Ah. Crap. All of his attacks are like done in the dead center of the screen. Ooh. Really? I was all the way down there and I still got freaking hit. Come on, come on. Just die, man. Just die.  Like right there. That's so difficult to dodge. What if I'm down here? Ooh, watch out. What if I'm down here? Oh, well, that was easy. Seed is incomplete. All right, hold a nest to skip. Oh! Um... Glitch trap? Is this you, my man? You're looking interesting. I'll tell you that. I've got 50 health. Um... And you're not doing anything. So... What's up? You want to... You want to talk about this? And I closed off the game. What is going on? This is the weirdest ending to a fan game ever. Or just a regular game in general. This is the weirdest ending. I didn't get to play as Kandy! Or did I? No, no, I didn't. Never mind. I did. I did. I'm pleased. I'm pleased. Really? Huh. Well... Interesting. Wait, Kandy had a voice? Wait, Kandy had a voice? Wait, all these guys had voices? I really hope this isn't copyrighted music. Um... This was an interesting game. Obviously. Um, just because it wasn't fully completed. But um... Yeah. I liked it. I did like it. I got a little bit mad at some points. But that's just because... It was just not a complete game. Basically, the only thing that's... You know... Um... What am I trying to say here? The only thing weighing it down is that it wasn't fully completed. Is what I'm trying to say. Other than that, really good game. Really enjoyed it. Turn of creation. Twisted reality. Nightmare madness. Dayshift of Freddy's. Dayshift of Freddy's. Oh, lovely. Oh, this is nice. Judy Bates, Skyler. Yeah, www.saintjew.org. Boys, if you have money to spare, I'm actually... I'm gonna make a note of myself on the whiteboard to remember to link Saint Jude in the description. So if you do have money to spare, you know where to put it. Alright, there we go. On the board, hopefully I don't forget. If I do... If there's someone that's watched this for, please tell me to do that. Yeah. Is that it, though? Just a black screen. This game isn't done yet, by the way. There are some secret minigames that we can play. Well, I say secret. They're in the extras menu. They're really not that secret. And you get the extras menu on, like, day one. So, um, yeah. Don't really know what's going on right now, but I'll wait. I'll wait. Alright, as great as this song is, it's been going on for a long time. It would be interesting if there's something on screen, but there was not. I really don't want to close out of the game, in case I miss something, so... I'm just gonna close out of the game, and I'll release it on it. Hopefully I didn't lose anything too precious. But again, this was a great game. The only thing weighing it down was that it was incomplete, and I fully understand the developer wanting to move on to other things. I fully respect that. Again, I had a great time. Hopefully you guys had a great time watching. I'm gonna see if there's anything new. Nope, we have just the extras. Um, and these sub-games... Yeah, these sub-games will take a look at next episode. So, thanks for watching, and I'll see you all on the flip side. Goodbye.


I could help draw a plan because that way that way you can follow the plan when you build it. And good morning everybody that's right reading the book about the New York City Marathon A Race Like No Other. We will see in case you are unaware in yesterday's vlog I announced that yes my next marathon it's crazy is the New York City Marathon in nine days from now so we'll see if I can get through the book in the next nine days but speaking of New York you're probably wondering what my race strategy is I will be sharing more about it next week I just want to say here is the elevation chart of the race so it's not a flat course because you cross all these bridges in fact you gain and lose 950 feet of elevation gain and loss 950 feet like that's you know that's that's a good chunk but if you notice the top left corner of this graph that a good bit about what I'm looking at is about 200 to 250 feet of elevation gain at the beginning which makes me really excited oh going over the Verrazano bridge so my legs will be fresh at the beginning of the race and you knock out just a good chunk right at the beginning of the race and then you got you got to use that downhill on the backside but I'm going to talk very soon about my strategy about my pacing I promise I promise I learned my lesson in Amsterdam I've got some thoughts and ideas on how I will pace the race in New York City but it's it's actually incredibly exciting to think about going out not with Michael Butter or Miquel Butter from and the reason I'm standing here is because I'm digging out clothes for my run today yes it did snow last night and I'm catching up on laundry we're catching up on laundry after Europe but Michael Butter who was the pacemaker in Amsterdam he is racing New York City he was actually pacing Amsterdam I think he went to 30k and then dropped and did a little workout afterward but that was his kind of big tune up for New York City so he's but I promise I'm not going with Michael Butter I'm letting him go I'm not going to run with him so anyway here we go it's cold out so I'm definitely going to be dressing a little warmer than usual okay what a day what a day here not winning any fashion contest today all right I need some strong boys to move the big box that arrived come on now you guys got that you got it we need your muscles no no no it's in the it's in the bedroom there you go oh our room there you go can you go get the big box straight ahead there it is oh yeah bring that too oh boy can you even move it you may have just lay it down and then and then slide it perfect now push it from the back you guys got it you've got it keep pushing push from the back there you go what are they doing keep going all the way to the coffee table all the way to the coffee table perfect okay you guys you guys go sit sit on the couch oh there you go okay here we go here we go definitely everyone the biggest running gearbox of 2019 has arrived all right let me let me get the big trusty knife stand back everyone this is my elf knife here we go all right what do you guys think it is any guesses oh ready one two three what is it oh America America oh my my here we go oh my gosh we're going to the world we're going to the ship we're going to the ship the world championship bag not too shabby right we're going to use this the rest of our lives holy smokes so everyone and you guys more more importantly the boys have a new rocket ship guys go you can you can go decorate it thank boys right now say thank you USA track and field hold on hold on now see it track and field there we go there we go there we go hun pretty cool let's let's see let's see what's inside oh my my all right all right let's see here hold on okay this is so cool just this just the suitcase we're happy we don't even need to know what's inside all right shall we okay let's the boys are preoccupied michael's preoccupied all right ready one two three oh the singlets oh my my oh honey look at that singlet look at that singlet USA oh my this is USA oh that way so here we go everyone the USA singlet i'll put it on for you later oh my what do you think michael what do you think USA oh another hat you know how i like running hats oh my goodness feel good look good feel good you know how they you know what they say look good race good so here we are and just so you know i qualify for all the new folks out there qualified for the us i've qualified for the world mountain running championships about three or four weeks ago in new hampshire so i will be representing the united states of america in argentina on november 15th am i racing the 15th november 15th in argentina so uh i'm a mountain runner at heart attempting to race marathons as well so that's so amazing this is like the best Christmas Christmas so right a little tracksuit let's up in front that you get from the high school gym so even though i am getting ready for the new york city marathon i'm really excited about the development of speed on the roads and the turnover uh for mountain running and the race i'm doing in argentina it's only it's like a little over seven miles so it's not that it's a short race so having speed is good it's really really good so i'm very happy about that hun you're gonna open that up set here i do want to see i do want to see a pair of shorts okay i got a pair oh and nice that let's look what you take to the oh yeah thank you thank you oh my gosh these are really serious wow okay i love all the colors i love right haul i love it i love it true love approves yes i do true love approves so bada bing bada boom all right there we go we got it all packed up and thank you usa track and field for taking care of us this was not expected i didn't realize the bag was going to be so nice or that the gear was going to be so nice this is beyond epic so thank you again and last little message is keep dreaming right inside this world is a lot better when we're dreaming and we're chasing down goals and uh overcoming challenges that pop up in our training or in races like in amsterdam like that was a learning moment for me but um i was a 16 27 guy in high school for the 5k in cross country and it's a it's a decent time but it's it's not you know it's not going to break any records let's just put it that way um but then with consistency passion and um listening to the body and taking you know taking little risks along the along the journey over years not over months or six months or two or three training blocks but over years of running has led to this showing up at the house so that's my little final message is just don't give up on what and big dreams and little dreams you know it's i um yeah it's those little ones that are almost just as sweet as the big ones so usa usa oh so fun ladies and gentlemen stick a fork in me i am done oh i am so tired definitely still recovering from the uh it's from amsterdam from the marathon but uh the jet lag or i don't know i i my sleep has been pretty good since returning but i definitely need a really good night's sleep right now it is six thirty p.m and i think i'm gonna go to bed soon so uh ran today i did go five miles seven thirty five a mile there it is in kilometers on your screen and um so what else was i gonna tell you i don't even remember because i'm so tired all i know is i love you oh yeah that was a little rendition of our dinner time it's always exciting at the dinner table you know it's always exciting um okay question of the day what is a little dream or goal that you have uh and that you want to accomplish before the end of 2019 all right you know got a couple months left a little over a couple months so it's time to figure out um do i have a goal that i said at the beginning of the year and it could be a little you know it doesn't have to be a big goal just a little one um let it share down below because i know i actually should go back and review some of my goals for 2019 to see how i'm doing so anyway that's the question of the day thanks for being here thanks for watching you guys rock and uh we're gonna keep fighting keep fighting keep keep sleeping you gotta it's good to fight it's good to sleep all right toss it back to a couple old vlogs one from 2018 because there's a lot of new vlog uh subscribers so that will be on the right and this is just a throwback vlog from last year and then on the left we'll toss it back to a recovery vlog where i talk about tips for recovery after tough races all right there you go see beauty work hard and love each other see you tomorrow


What we're here to do is try to educate people about how Formula E can contribute to the evolution of the electric vehicle. Racing is such a great environment for high-speed and high-paced development that will contribute to making better electric vehicles in the future.