sick. So you have to just have some patience here. So everybody here today, were you all here on Tuesday? You all got the syllabus? Anybody? Okay. There's nobody that ran? Okay. So I will not say anything about that. You heard my spiel on Tuesday. I was a little incoherent. So I had a high fever. I didn't even know. But hopefully I didn't, I made some sense. Okay. So just to remind you real quick, the first assignment, I just want to reiterate this, just to make sure everyone's totally clear on this. On the syllabus it says that it's due on Tuesday. The first assignment will be due on Thursday. So one week from today. You're just going to have 1.1. I'm going to give you the assignment today at the end of class. And then on Tuesday we'll just, probably we're going to start some new material, but I'll definitely save some time on Tuesday to go over some problems and just get you situated and comfortable hopefully with how to do these induction proofs and such. Just out of curiosity before we started, how many of you have seen induction before? I've done induction proofs before. Okay. Somewhat at least. Most of you have, okay. Probably from discrete math, you took discrete math and you probably covered this in discrete. I would hope at some point. So we're going to start from the, sort of the very beginning. I'm even going to start sort of in some sense below induction. So a lot of this is not actually in section 1.1 in the book. It's actually sort of preliminary stuff. So this will be probably a review for most of you, but I figured it's, can't hurt just to cover all the basics before we get into some more difficult stuff. So if I can figure this out. Let's see here. These lectures will be available online. Yes. So they should be accessible through Blackboard. Okay. So there's, yeah. I'll tell you what. So I don't want to spend too much time on this here in class to get through this stuff. I'll send an email out about this. Okay. So I'll just email you all this. And Joe, I got your email. It's, the course is accessible now through Blackboard. Okay. So, okay. So let's see. All right. Let's see if this works here. Okay. Okay. I guess I didn't want to do that. Okay. Sorry. Thank you. I need, I need all the help I can get here. So I think this is, yes, it's on now. Thanks for that. Okay. And let me see if this will work. Okay. Oh, okay. Great. This is, okay. This is, I've never done this before. So this is still going to be, yeah, this is, this is weird. Okay. All right. Let's see here. With this. Okay. Well, unfortunately, I have to do this. So, okay. Let me see if I can, oh man, this is really crazy. Okay. No, I'll get, I'll get the hang of it here in a second. I cannot see it on the tablet. I can only see it on the screen. Okay. All right. This, this, I, I'm praying that this gets better at some point as we go through this. Oh man, this is weird. Okay. Let's see here. Okay. So, yeah. Okay. All right. All right. All right. Yeah. Okay. This is harder than, than it looks. Believe me. Okay. Let me draw on it. Yeah. Okay. Okay. Okay. Wow. This is, this is weird. Okay. This is, stands for definition. Okay. D-E-F. Okay. Okay. I'm just going to go slowly here and then maybe that'll be, make this easier. Set. Okay. You've all seen this word before. Informally is, this is getting better, a collection. Okay. This of course is very fundamental stuff. We're going to be talking about sets. In this case, it's usually going to be sets of numbers, but it doesn't always have to be. These, these objects can be anything really. Okay. So, if is a set B, let's say, is the objects, right. Probably seen this notation before. I'm going to align that. Sorry. That's supposed to, yeah. Okay. That's supposed to be a D. Good. Good. Okay. This will get better. I promise. Okay. Okay. That should be denote. Okay. This, if you've never done this before, trust me, it's not as easy as it is. Because you can't, when you're writing on this, you can't see it. You can only see it on the, on the screen. So it just, it makes it, it makes it very difficult. Okay. So, now I, you guys come up here and try it. I, I promise you, it's not easy. Okay. So have you guys seen this before? This, okay. This Greek letter, epsilon. Okay. Okay. So, all right. So then B is said to be a member of an element of X. Okay. And the thing is, my handwriting, if I was on the board, is so neat. I have the best handwriting you would ever, ever hope to see. It's not a joke. Okay. If I had sloppy handwriting, this would be disastrous. Yeah. Okay. I wish. I wish. Well, that's true. Although I'm going to, yeah. It would be, yeah. The problem is that there's going to be so many, so many, as we go along, there's going to be so many mathematical symbols that it's going to, it's going to be tricky. Yeah, I could do that. I could do that. But I, well, you guys can read this though, right? I mean, it's readable at least. Yeah. Okay. Okay. So let me, let me try to squeeze this in here. Okay. If, yeah. I'm going to, actually, I may end up doing that at some point, but I'd like to get comfortable with writing on this first. Okay. So B is not an element of X. Then we see if I have enough room down here. Then we write this. Okay. Hopefully I don't screw this up too badly. Yes. Okay. That's one with a little strike through it. Okay. Well, this doesn't look very good, but hopefully this will get better here as we go along. Okay. So you guys can at least, I'm sure it looks much better in your notes. So there we go. Did everybody have that down? I should have asked that first. Okay. I can go back if I need to. So I'm having a little trouble following this because it's coming in pieces. Okay. What you have up there is the definition of set membership. Yes. Set membership. B is a member of a set X. Then you just write B epsilon X. If it's not, then it's B epsilon with a slash through it X. Yes. Yes. Okay. So let's just do a quick example here. And by the way, you'll see what the abbreviations are here in a second. But EX, I'm going to use this a lot. This will just abbreviate example. And I'll try to have them numbered as, you know, sequentially as we go through. Okay. And again, I realized this stuff is all stuff that you've seen before, but I just want to get a really nice slow introduction to everything that we're going to do. Okay. Okay. So in this case, X is just the set, the numbers one, two, and three, of course. And really the only reason why I'm doing this example is just to remind you of what the standard notation is for representing a set, especially just a set of finitely many members. For example, in this case, of course, we just have three members. Okay. And so just with the notation that I gave you before, the definition of membership. One is an element of X. Two is an element of X. And three, okay, no, got it weird again. Okay. It's an element of X. But for example, for example, zero is not an element of X. That's easy enough. So that should be pretty clear. I know I'm probably boring you with this. It's so, so simple, but I just want to make sure everyone's aware of this notation. There. Everyone clear on this? Super easy, right? Okay. Okay. So if a set X is finite, so we'll often represent X the same way as we did in the previous example. Okay. So we'll just list the elements as in example one with the elements separated by commas. Also, and this, you'll see this a lot in the text, too. And a similar convention will apply to sets whose, sorry, whose members a clear path. Okay. So some of the examples I'm going to give you are going to be sets that we're going to be studying in this course. This looks like how I wrote when I was five. Is that right? Okay. But they write like this on the white board, though. Yeah. No.  What's that? Well, no, I mean, it's much, much better than this. Yeah, no, that's, that's, I'm hoping that happens in the next couple of days, actually. Exactly. Okay. I assume I gave you enough time to copy all of that down when we were laughing about how bad my writing is. Okay. Okay. So, let's see here. All right. Second example. So, and this, this you've probably seen before. So we're going to call this, you know, Z with a sort of a line in the middle here. Okay. So we've got the, the left parentheses. So these, we've got some dots just indicating that the pattern continues. Again, you've probably seen this before. So in this case, again, just to remind you, note. Okay. So again, I assume you've seen this before, but these, these sort of these, this ellipsis on both sides just means that the pattern continues. Right. So for example, the number 10, of course, is an element of the set Z. Right. You know, you guys believe this, hopefully. That should be hopefully pretty self-explanatory here. Yes. So in the script for like integers, the Z would like you go like that and then the line would play if we wrote it that way. Oh, I see. So you had the, you had it sort of diagonally instead of horizontally. Yeah. Oh, yeah. I mean, as long as it's clear what, what you're talking about, I mean, the, the, there are, there are some conventions that are not uniform. So, yeah, that's, that's fine. Okay. That's fine. Yeah. Yeah. I mean, the, the standard, at least from, you know, textbooks generally have it as a sort of blocky Z. But whatever is, I mean, as long as it, as long as there's a Z hiding in there somewhere, it's, it's, I'm not, you know, I'll be able to understand what you mean. Yeah. Okay. So, so the set Z is called the set of integers. Right. I assume you were all familiar with this set before I told you this, I'm assuming. Okay. So another example. This is, of course, the set of integers is, is going to be a set that we're going to be studying quite a bit in this number three course. And in this case, which you've also seen in discreet probably. Okay. So the set capital in is the set of, okay. What, what, what, see if you remember this. What is this called? Natural. Yes. Natural numbers. Well, yeah, that's something else I'm going to mention here, too. Here's the, the issue that the set of natural numbers, it depends on the textbook that you have. There are many textbooks that include zero as a member of the natural numbers. I'm, unless there's something that is just plain wrong, I generally try to follow the textbook that I have for the course. In this text, the author defines the natural numbers to be the set of positive integers. So not including zero. I would say in this case, in modern mathematics now, I think the majority of authors actually include zero as a natural number, but yes, Z also has the negatives. That's right. But like I said, there's no huge harm being done here. It's just, you know, we're just going to set this being consistent with the, with the author as a convention in this course to not include zero as a natural number. So just something to be aware of. So I'll just say this below here just to be complete. So the natural, the set N, the natural numbers is the set of positive integers. Actually, I think my writing's improving slightly already. I think, yeah, it is a little bit. So hopefully, yeah, hopefully in another week it'll look really good. Okay. Are we okay with this then? You guys got this down there? Yeah. Okay.  Okay, we underlined that. Of Y provided. So what's this, what is this definition? So we want to finish this off for me. Every, every element of X is an element of Y, right? Sorry. Okay. You can read that element. Okay. That's good enough. And so you've probably seen this notation before. That's a D by the way. Okay. Denoted like this. Okay. Have you seen this notation before too? Subset. Okay. Okay. So like I said, I'm, I am starting off here with, with just basic, basic principles. Okay. So we've talked about notation for sets, especially finite sets or sets that whose members follow up certain pattern. So for example, set on the left is certainly a subset of the set on the right, because you can just check that all the members on the left are also members of the set on the right, right? Ordering of course makes no difference. When we're talking about sets, the order doesn't matter. The set, if I want to write the set 0 comma 1 comma 2, if I want to write it 2 comma 1 comma 0, it means the same thing. Okay. So there's no sort of sense of order built into a set. There are ways in which you can, you can sort of build order out of sets, but we probably won't get into that in this course. Okay. So another simple example. Okay. So we talked about these sets before, right? Okay. That should be clear. The natural numbers, it's a set of positive integers. So of course every natural number is an integer. So this is, this is pretty clear. Okay. So let's do a couple more examples. This is, you're going to see this notation so much that I just want to make sure that everyone's on board with this, especially, and I know a few of you in here haven't, haven't seen discrete math in a long time. So I just want to make sure everyone's, you know, up to speed on this. Okay. So this is something, I was going to write this out as a definition, but because we got started a little bit late, I'm, I'm going to skip this, but you, I think I've all seen this before. Okay. So what I'm writing now is the set consisting of the natural numbers n little n in capital N with the property that little n is prime. Okay. So this is another way of expressing more compactly a set that if we were to write everything out, of course we wouldn't ever be able to finish because there's an infinite number of elements in the set. So often what we'll do to express a subset of a given set is we will say, we'll look at all the elements of a certain set that have a given property. And so in this case, if we, if we look at the set of all natural numbers n that are prime, okay. And so let me just explain this again. When you see this notation, if any of you aren't familiar with this, this on the left side, what this is saying is n and n, the, the, the colon you should interpret as such that. Okay. So if you haven't seen that before, if you want to write that down, it's the natural numbers n and n such that n is prime. Or with the property that. Okay. That's, that's what that means. And so of course you all know what, what prime numbers are. Now we're going to, this is going to be a, certainly a focal point of study in this course. So for example, in this case, we would have two, three, five, seven. Right. And on down. And the dots mean of course that the pattern is that we're just can, we're just building up the prime numbers this way. Right. So it would be the next number in this set. Seven. Yeah. So 11 would be the next number. Right. 13. Right. We just keep going that way. Okay. So this is something that let me, let me give you a slightly more, a longer example here, but okay. So what about this x in z now? So remember what this means z is the integer. So again, I want to, maybe I should have gone a little more slowly through the last example, but this, so far what you wouldn't interpret this as is this, the set of integers such that, and I'm going to list some property. Okay. And so it's, here's the property x is less than zero and x equals y squared or some, wanted to get that on one line, for some y in z. And so I'm going to be a little bit ambiguous here and say equals and then the question mark. Okay. So I, what I really, the point of this example really is just to get you to think about what this is saying. I just want you all, hopefully all to, to just understand what, what this is. Okay. So this is the set of all integers x with the property that x is negative. Right. And it's the square of some other integer. And so can you think of any integers that have this property? Well, okay. Well, let's see. It's going to be, yeah, any, any real number squared is going to have to be bigger than or equal to zero. So what can you say about this set? Well, yeah, so I mean, it's, it's the empty set. It's the empty set. Right. So, right, null set or the empty set both mean the same thing. Right. So this, and then I'm going to give you, of course, the, the definition here in the second two, but, which I'll also define here in a second. Yes. Well, well, why isn't it this, the set of numbers that have integer square roots? Well, because the, well, first of all, this, the definition of the set is that if there was anything in this. Yes. That's what I was going to say. Yeah. It's net x is less than zero. Okay. Are we okay with this? Yeah. Okay. Good. Okay. And so that brings us to the next definition, definition for the set with no members called the empty set. And the typical way to denote this is with, is by zero with a little slash through it. Okay. Is this something you guys have seen? Seen this before? Yeah. Oh, no. I mean, so if you, if you, if you put brackets around it, then it's not empty because the empty set is a member of that set. Okay. So, yeah, you don't want to put brackets around it. If someone told you that before, that's, no, no, no. Okay. No. That is not the standard convention. Definitely not. Because, and that's a good question though, but just with the convention of enclosing a set with finally many elements and brackets, if you put the empty set in brackets, then the empty set is a member of the set containing the empty set. So with the bracket, well, the set, if you, if you put brackets around it, then that's a set with one element, the empty set itself. Okay. Yes. Okay. But no, I'm glad that you asked that. Yeah. The empty set is just, this is it. That's it. That's how you denote it. Okay. So now, how do you know, and this, this is really is a definition. How do you know when two sets are equal? Well, okay. Hang on one second, Joe. I thought you were asking. Oh, well, I was sort of rhetorical, but you, no, but you can answer it. It's okay. Right. Yes. That's, that is exactly right. So two sets X and Y are equal. Oh, well, that did not mean to do that. Okay. Yeah. Let's, let's see. I don't, I don't, okay. Okay. Oh, okay. Yeah. Yeah. I see it. I see it. Okay. Let me, let me try this. Okay. Okay. Which is the, which one is the eraser now? This one? Okay. So then, do you really erase the, no, I do not want to do that. Yeah. Let's see if that, let's see if it works. Let's see. Okay. I don't know if this is going to, no, it doesn't, it doesn't, no. Okay. Okay. Tap all this right here. No, that doesn't work either. Yeah. Okay. I could do that too. Yeah. Where's the, where's the color? Oh, I see it. Yeah. Okay. There's got to be a more efficient way to do it than this, but okay. Well, that's one way to do it. Okay. Yeah. Yeah. No, I got that. I got that. Yeah. Sorry. I still have a fever of like 102 or something right now. So I'm still not totally with it yet today. So that's another reason why it's, maybe I'm not, I feel a little delirious still. Okay. Okay. So there we go. Two sets x and y are equal. I'm glad at least this is, this is readable. So let's see. You guys can still read this, right? You can, I mean, sure. Okay. Good. If they have the same members. So what's another way of saying this? Well, okay. It means every member of x is a member, if they have the same members, then of course every member of x is a member of y. And conversely, every member of y is a member of x. So another way of saying this is that x is a subset of y and y is a subset of x. Okay. So now let's do another example here. Let's see where we add. I think we're on eight now. If I'm not mistaken. Example eight. Okay. So this will make you think just a little bit. Let's let the set x be the set of all, so I'm going to remind you what this means. The set of all natural numbers such that, right? That's what this means. Little n epsilon capital N colon. Set of all natural numbers such that there exists real number or such that n equals, okay, n equals x squared. Okay. So here I'm going to ask you two questions. Sub question one, if you will. This shouldn't require too much thought. Why is this true? What's the question? Is x a subset of n? Is x a subset of the natural numbers? The answer doesn't come to you right away. It's because it's so easy. It's flying over your head. It's a subset of the natural numbers just by definition because it's a set of all natural numbers with a certain property. So anything in there by definition is a natural number. Okay. That's just how it's defined. So the answer to this question is definitely yes. And all I really need to say here is this is true just by definition. Okay. So we talked about the natural numbers. I haven't explicitly talked about the real numbers, but with your experience with discrete math and calculus and such, I'm sure you're roughly familiar with what these are. Okay. Second question is the set of natural numbers, a subset of this set x. Okay. So now the question becomes, remember what this notation means, subset means is every natural number an element of x? Okay. The definition of x? The x is a set of all natural numbers with the property that it's a set of all natural numbers n with the property that there exists a real number x such that n equals x squared. Anyone want to, what do you think? Yes? No? Not sure? No? Some people say yes. Some people say no? Okay. Yes. If n is a subset of x. Well, let's see. Let's see. Okay. Let's let n be just any natural number. Okay. Hopefully, I'm going to convince you of this. What the right answer is. Do you guys buy that? Okay. Let n be any natural number. Then n is certainly equal to the square root of n squared. Okay. Now the square root of n is in general not going to be a natural number, right? If n's a perfect square, then it's going to be a natural number. But what can we say about, but we don't need that. That's not what we say. And the definition of x doesn't require that. Right? So to be an x, all we need is for n to be some real number squared. Right? That's, if you look at the definition of x, some real number squared. And since every natural number n is the square root of n squared and since the square root of n is real, right? Because n's not negative. Remember the definition of the natural number is 1, 2, 3, 4, 5. Square root of n is real, so every natural number, since it's a square root of n squared, is equal to some real number squared. And the square root of n is real again because n's not negative. Make sense? Okay. Thus, I'm not going to write all of that out, but thus n is an element of x. The only part I didn't write down is the fact that the square root of n is real, and that again comes from the fact that n's not negative. That's the capital n. That's capital n. This is little n, this is little n. That's little n. But the one over there is capital. So what can we say? What's the relationship then between capital n and capital x? What can we say about these two sets? They are equal. Okay? x and capital n are the same sets because they're both contained in the other. So I'll write both of those things down. So we just showed that n was contained in x, hence n capital n equals capital x. Okay. Are you okay with that? Okay. And time's flying here. Okay. All right. What's that? I know. Yeah, I know. Okay. It'll get faster hopefully. Everyone has this down? Yeah. Okay. So now we are going to start talking about the last 20 minutes or so, because what your homework is going to be based on, and I realize I'm not going to get very far into this, but we'll do plenty of this on Tuesday. Okay. Induction. So now this is really where the text starts with this concept of mathematical induction. Okay. So before we get into this, let's do an example. Example nine. Let's let, and this is, again, this is going to be very easy, but seven, eight. Okay. So we're going to do the set containing seven, eight, nine, four, 10, 11, 12, 13. And we'll say we're just going to continue this pattern on down. My, these dots, I mean, I'm not going to skip back. I'm not going to go back down. It's going to be 11, 12, 13, 14, 15, 16. It's going to just continue to go forever that way. Well, sort of, and this looks like kind of a weird set, but I'm doing this on purpose. Okay. Do you, do you guys believe that this is true? You buy that? Okay. And the reason why I threw the four over here is just again to stress the fact that order does not matter here. Okay. Okay. So what number is the smallest number in this set? Yes. I realize this is very simple, but I'm just setting up what we're going to do here in a second. No, no, no, no, no. No. Yeah. I mean, that's, yes, and yes, you're correct about that. Well, that, that could happen, but, but yeah, I mean, it's, it's not going to be something. I'm not going to trick you and say, no, no, you know, 56, 57, and then three, you know, no, I wouldn't do that. No. Okay. So this is, this is so obvious. I think I'm not going to say anything about this. Okay. Now here is a very fundamental property of the natural numbers, which is called, and again, those of you who've taken discreet note know what this is. This is called the well ordering principle. Okay. And it says this every non empty. Okay. I'm going to underline that. Of course, it's clearly false if you have an empty set, but every non empty subset of the natural numbers capital N has a least element. Okay. So because of time, I really want to get through this. I may not write this down. So writing is really slow. So I'm trying to make it legible, but this, if you think about it, is something that should be intuitively obvious if you, if you just think about it for a second. Okay. And instead of writing the sound, I'm just going to say it. All right. So take your set S to be some non empty subset of the natural numbers. What I mean by non empty, I mean there's just a, there's at least one member in S. Okay. One element, at least one element of S. Okay. Well, if, if one is an element of S, then one has to be the least element of S, because there are no smaller natural numbers than one. So one's certainly the least element of S. If one's not, I'll assume one isn't an S. Well, suppose two is an S. Well, then two's the smallest one. Right? If two's, and one and two are both not an S. Well, three is an S and three has to be the smallest one, because one and two aren't there. And then you just keep doing this, right? And so eventually you're going to have to come to an element of S. The first one you come to, there's the least element. Okay. And again, you have to come to something at some point, because S is non empty. Right, right, right. I mean, yeah, it doesn't, so there's no, it doesn't sort of make sense to say that, you know, you have this set, for example, if I were to write, I'm not going to write this down, but left, you know, bracket two comma two comma two right bracket, that is just the set containing two. Okay. So, yeah, I mean, this kind of stuff doesn't, doesn't happen. Yeah. Okay. So, hopefully that you guys buy, buy that. I don't think that's too hard to wrap your mind around. I think that's pretty clear. Right. Okay. So, here's what the last thing I'm going to get to today is just called the, I think I'll go ahead and do this on a, on a new page here. And this is a, this is actually a theorem that we can, we can prove from this well ordering principle, theorem one. And so the book calls this the first principle of finite induction. That's kind of a non standard terminology, but that's okay. Okay. Oops, sorry. Yeah, that's all. There's something in, I've been working on, there's something in mathematics called a principal ideal domain. And I've been working on these all day long. That's why, that's why, that's why I spelled it this way. I know how to spell it just, it's just the other mathematical object is a L instead of LE. So I was just on autopilot there. Sorry about that. We're not going to be dealing with these things in here. No, no. Okay. Now, principal ideal domains are great, but no, no, but now these things come up all the time in abstract algebra. If you go into abstract algebra, you'll learn about these things. Okay. And here's what it says. So suppose that s, and this is why I kind of did the background with sets and subsets, because now you know what all these things mean. s is a subset of the natural numbers. And suppose that s has the following, so first property is very easy. First property is just that one is an element of s. Second property is that, and I'm going to write it out in a really, well, lengthy way, but I'm going to underline the relevant words here for all natural numbers. If, if n is an element of s, then n plus one is an element of s. Okay. So that's the hypothesis. Okay. So again, I'm guessing the majority of you have seen this before. What's the conclusion? If s is a subset of the natural numbers with these two properties, what can we conclude about s? Then anybody remember this? Yes. Then s is equal to a set of natural numbers. That's right. And so what I'm going to do, and unfortunately, I may only have time to do this today. At least I'm talking about the principle of finite induction. I'm going to try to give you a sort of a informal heuristic argument to again convince you or to get a feel for why this is true. I probably won't get to this now, but next week I certainly will. I'll give you the formal proof of this from the well-ordering principle, and then we'll talk about how to write induction proofs and we'll start talking about how to prove things about the natural numbers. That's going to be part of your homework assignment that'll be due next Thursday. We're not going to get into a lot of that today. Like I said, we're going to run out of time. But what I'm going to do is, oh gee, let's see. I might have to write kind of small here, but I want to leave this up here. So the first thing I want to tell you about is what I'm just going to call an informal argument to just try to convince you of this. And I think I will. If you pay attention to this, I think I'll convince all of you that this is true. And this won't take long. And then I'll give you the homework, and then we'll stop for today. So I'm just going to ask you a few questions, and hopefully I can squeeze all these in here. Question one. Okay, now we're assuming, so I don't have room to write all of this down, but we're assuming that s is a subset of n with the following two properties. And what I'm trying to do is I'm going to try to convince you that s has to be all of n. So we're assuming s has property one and property two. So the first question is, well, what's the smallest natural number? One, right? We talked about this, right? Natural numbers are positive integers. One is the smallest. First question is, is one an element of s? Okay, why? Property one, right? We're assuming these two properties about s. So by property one, one is an s. We're just assuming that s has that property, right? So yes, by question two is two an element of s. Okay, now here is what I want to be very clear about this property two. It may be the intuition may be marred a little bit just by the length of the statement. What is property two really saying? Here's all it's saying. Here's what property two is saying. It says that if you have a natural number that you know is an s, then the next natural number is an s. That's what it says, okay? So if you know something's in there, then its successor is in there too, okay? One is in there. We just established that by property one. So therefore by property two, remember what property two says. It says if we have something in there, then the next guy is in there. So since one is in there, we already know one is in there, therefore two is in there by property two. Yeah, well yeah, exactly, and that's right, and that's exactly what I'm trying to get at now. Right, so yeah, I'm just trying to do this slowly so everybody catches on to this principle. No, no, no, I mean that's exactly what- No, no, no, no, it's fine. I'm hoping that this is something that's becoming more transparent now. So now from the second part, question two, we know that two is an s, and therefore by condition two that we've imposed on s, whenever we know something's in there, the next one's in there, since we know two is in there, three is in there. Now that we know that three is in there, by property two, four is in there. Now that we know four is in there, by property two, five is in there. You see that? So everything is going to be in there, okay? I'm running out of room here, so when I say by two, I mean, really I mean by two, and the affirmative answers to question one and two, therefore three is an s, and then you just continue to carry this down, okay? And so that's what I'm running out of room here, but let me just write that down. Dot, dot, dot, or you can write it vertically if you want to. Continuing this argument, it should be, hopefully I've convinced you that yes, s has to be all of the natural numbers. Does that make sense? Okay. Anybody not okay with this? Okay. Now of course the trick here is using this property now to prove theorems about the natural numbers, which of course, we don't have time to get into today. I'm going to give you the homework that'll be due next Thursday. Again, I'm aware that we haven't gone into the problems that you're going to be encountering in the homework yet. I'm assuming how many of you have actually done proofs by induction? I know I asked about induction before, but you've done proofs by induction. Okay. So most of you are already familiar with how these sorts of things go, and that's really the content of the homework that I'm going to give you. Tuesday, just so you know, Tuesday, what I'm going to do is I'm going to demonstrate how you use induction to prove certain statements about the natural numbers. So if you're still kind of foggy on some of this, Tuesday's lecture should really get you up to speed on the homework, which you'll still have two more days to work on. And I'm not giving you a ton of problems here for the first assignment. So let me give you the homework, and I guess that will be it for today. Okay, so from the text, homework is section 1.1. So I'm going to give you problem 1a. So problem 1 has a lot of parts to it. 1b, 2, 9, 10, and 14. Okay, so this is due, again, I guess that should be what, the 31st, I believe. Okay, so this will be very clear here. This will be due Thursday at the beginning of class. Okay, if I don't want you working on the homework during class, when I'm talking about new stuff, so make sure they have it done by the time you get in to class.


What's up everyone? It's your girl, Kenty here from Waitin' Sports Cards, and I am rippin' a personnel here for Dillon P. We've got a 2021 Top Scrum Update Sapphire Edition Baseball Box. Alrighty Dillon, best of luck. Thanks so much for your order, and let's see what we can get ya. 2021 Top Scrum Sapphire Update. Let's see a big rookie Otto here. Where's everybody at? Still sleepin'? I don't blame ya. Three-day weekend. Again, every one of these cards Dillon will get sleep in the top load before him. And we've got our Otto already. How about a rookie of Andrew Vaughn? There you go. Nice rookie Otto there for the White Sox. Andrew Vaughn. Very first pack. Paxton and a Sierra. Cisco, we've got Dillon Tate, and rookie of Ben Bowden. Anky Legend going first. I'm gonna order a lead best of sports. Oh awesome. I'm excited to rip that. You know what? Rookie, Kelly, Rich Hill, and a Romano. Remember opening that one year and pulling like a Kobe Game East jersey out of two or something? It was crazy. Jose Devers rookie. We've got rookie debut, Jazz Chisholm Jr. Daryl and Daly Oln. Like I like the multi-sport stuff because you really never know what you're gonna pull out of there. We've got Khalil Lee rookie for the Metz Green rookie of Angel Rendon. Three cardinals. 25 out of 50. What's up kitty? Happy Sunday to you as well. Let's you see and a Spencer Howard rookie debut. Got rookie Chris Rodriguez. A Kyle Isbell rookie. Keegan Thompson rookie and Jock Patterson. Nice pack there. Three rookies. A couple packs left here for Ian Dillon. Bradley Jr., Talian, a Brock Holtz, and a Chris Owings. Last pack here for you. Got rookie Brian Garcia. Tom Rookie for the Pirates. Farmer and Nick Nelson rookie for the Yankees. Alrighty Dillon, that will do it for your box. Congrats again on those hits. Thanks for hopping in and we'll get them right out to you.


So, let us do an example of a Bayesian Bayesian game and let us see how the how a Bayesian Nash equilibrium we will compute a Bayesian Nash equilibrium of this game in mixed strategies ok. So, the game here has two players let us denote these players by 1 and 2 ok. Now player 1 has player 1 here as has two types let us denote these types by I 1 and I 2 and player player 2 has just one type and that is just denoted by is just this ok all right. Now, these types get realized with probability half. So, probability that of this is equal to probability of this is half ok all right. Now, there are two possible actions for the players ok so, let us player 2 player 1 there are two possible actions for the players. So, player 2 has actions L and R and these actions are the same regardless of are the same in the I mean since player 2 has only one type ok he has just this one set of actions which is L and R, but for player 1 because he has two possible types the action set also depends on his type ok. So, here he has actions so, when his type is when the type profile is 11 comma 2 when that is the type profile he has two actions let us call them up 1 and down 1 and the payoffs are 1 0 0 2 0 3 and 1 0 and when the when the type profile is 1 2 comma 2 you have the actions up to down to and what are the actions for player 2 it is still L and R right because he has he is actually has only one type ok and the payoffs then are 0 2 1 1 1 0 and 0 2 and both players are maximizing ok both maximizing players all right. So, let us write out this game in extensive form so, you have nature which is playing with so, nature chooses a type 1 1 for player 1 that is one other type 1 2 for player 1 ok. Now then player 1 has two choices which is up 1 down 1 up 2 down 2 player 3 player then comes this is player 1 then player 2 will play player 2 has two actions left and right now what is the information set of player 2 here what does player 2 know so, it is a simultaneous move game after the types have been realized so, what does the player know player knows only his own type right and plus it is a simultaneous move game so, what is his information set everything in one this so, he has this information set right so, you so, the information set of player 2 is this now let us write go back here and we need to write out mixed strategies for the player ok. Now player 2 has only one information set so, he can randomize so, you think of it as not mixed strategy behavioral strategy so, for this information set he is going to choose he is going to randomize between L and R ok suppose he chooses L with probability Q and R with probability 1 minus Q so, it is going to so, remember this so, you have L with write this in a different color so, L is chosen with probability Q R is chosen with probability 1 minus Q what about L and R here it would have to be the same because there is only one information set so, this Q and 1 minus Q ok now, what about player 1 player 1 can be allowed to randomize differently in each matrix right so, here he can he let us say chooses X and 1 minus X and Y and 1 minus Y ok so, if you remember what we what we discussed about these for these games what happens effectively is that this becomes a game in a Bayesian Nash equilibrium becomes equivalent to a Nash equilibrium in which every type of every player is a distinct player so, because now there are there are a total of 3 types one for player 2 and 2 for player 1 is this effectively now looking for a Nash equilibrium as a for a 3 player game this is clear that is what we are effectively looking for ok so, you can imagine this is going to be quite complicated because it is anyway 2 player game is itself complicated 3 player game means that we have to now solve for these 3 variables X Y and Q simultaneously ok and so, this is just a way to just to give you a flavor of how you can go about doing some calculations like this so, I will just go through these arguments one by one so, first let us argue to find this now so, first let us argue that Q has to be Q cannot be either 0 or 1 in an equilibrium so, first we show that Q cannot be either 0 or 1 so, what happens if let us say what happens if Q is 1 so, let us come back here ok if Q is 1 then basically player 2 is choosing L he is choosing L here and choosing L here also ok now if he is choosing L here what is the best response of player 1 in this type he would choose so, players are maximizing so, he would choose X equal to 1 right he would get 1 then ok now, but if he is choosing X equal and then his and what about the best response in this one he would choose Y equal to 0 right he would choose D 2 is this clear ok in that case if player 1 is choosing U 1 here and D 2 here ok now, what is the payoff that player 2 can get from this so, this type gets realized with probability half this type he gets realized with probability half right so, he is getting half times 0 plus half times 0, but if player 1 is going to be choosing U 1 here and D 2 here what should player 2 actually instead do player 2 can in fact play R instead of playing L right because then he will get 2 here so, in other words L is not if L is chosen by player 2 then player 1 would choose U 1 here and D 2 here ok in which case player 2 would get half would get 0, but then player 2 can shift to R and get something more than 0 for sure ok so, in other words playing Q equal to 1 is not a you cannot be an equilibrium alright likewise you can argue that Q equal to 0 also cannot be an equilibrium ok for the same you can come up with the same sort of argument so, if Q is equal to 0 then basically player 2 is playing player 2 is playing this R alright if player 2 is playing R then the best response for player 1 in this type is to play D 1 and in this type it is to play U 2 alright, but the best response to that is not R anymore ok so, you can check that ok. So, what this means is that so, if Q is equal to 0 must play U 1 comma D 2 which gives player 2 half of half of what half of 0 plus half of 0 which is 0 so, if Q equal to 1 this is with Q equal to 1 right similarly, if Q equal 0 player 1 must play must play what D 1 comma U 2 it gives what does it give player 2 half into 3 plus half into 1 which is 2 ok, but if player 1 is playing D 1 here and U 2 here so, if player 1 is playing D 1 so, instead in Q equal to 1 would have given him Q equal to 0 sorry I have been looking at the wrong block so, if Q is equal to 0 player 1 must play D 2 so, that gives him which gives player 2 what does it give him half into 0 plus half into 1 right yeah which is half instead playing Q equal to 1 would give him would give player 2 half into now half into 3 plus half into 2 right is that right half into into 2 which would be 5 by 2 ok. So, this shows that Q which means that Q is Q equal to Q is between 0 at a Bayesian Nash equilibrium alright ok. So, which means that player 2 is playing a completely mixed strategy with something that is between 0 and 1 which means then that we as far as if you look at which means that the payoff that player 2 can get from each of his pure strategies must be equal right because he is mixing between between them is mixing between them. So, it cannot be that any one of them has higher payoff that is what we have basically shown here right. So, which what this means is that so thus payoff of player 2 from each pure strategy L or R must be must be the same ok. So, what is the payoff that he gets from when he plays when he plays L. So, firstly the the first box is first type is going to be realized with probability half times now the he gets a payoff of 0. So, here this is chosen with probability X the box itself is chosen with probability half then this action is chosen with probability X right by player 1 that is X here. So, you are going to get half into 0 into X plus half into 3 into 1 minus X ok.  So, this is what he gets from this from this box and this and plus half of this what he would get from this box by by playing L ok. So, half into 2 Y plus half into 0 into 1 minus Y. So, this here is the from L remember what I am writing here is you of that the what the player would get when he knows his own type right. So, what you have to do is you have to sum over the types of all the other players times the probability that those types will occur given your own type times the payoff that will come and then there is also a mixing mixing mix strategy that is happening which is giving rise to these X's and Y's ok. So, you have also then the strategy the strategies that are chosen. So, that is what is written here ok. So, this is the payoff from L what is the payoff from R. So, this has to be equal to the payoff from R. So, this is half into half into 2 X plus half into 0 into 1 minus X plus now half into yeah half into 1 into Y plus half into 2 into 1 minus Y right. So, these 2 have to be equal now what this gives us is that X should be equal to 1 plus 3 Y by 5 ok. Now, this is a characteristic feature of these things that you get this kind of simultaneous equations across the types of players of the same player ok. So, which means that you must have that Q has to be between 0 and 1 and X has to be X is has to be equal to 1 plus 1 plus 3 Y by 5. Now, question is does every such is every such point actually an equilibrium is this enough. So, this is just we just know that this must be satisfied, but we do not know if this is you know this is if all such points are equilibrium ok. So, now, let us go through this let us let us drill down further into this. This is if we have narrowed it down to this now ok. Now, suppose so now let us take these cases. So, suppose Q is less than half if Q is less than half. So, we just know that Q has to be between 0 and 1 and and these which means that X and Y has to satisfy this. Now, whatever Q you choose X and Y should be a best response. Now, suppose Q is less than half ok what is player 1's best response. So, just go back to this if Q is less than half ok which means that Q is giving more weight to this ok. So, what is the what is player 1's best response? Yeah. So, is player 1's best response actually it turns out that X equal to if Q is less so you can write this out you can write out the exact thing ok. So, what is player 1 getting here? Here is getting Q plus 1 minus Q and here is getting sorry Q into 1 plus 0 into 1 minus Q here he is getting 0 into Q plus 1 into 1 minus Q right. So, if Q is less than half then player 1 would prefer this. So, which means X equal to 0 is his best response right and likewise what let us see here. So, if here he is get what is player 1 getting here he is getting 0 into 0 into Q plus 1 into 1 minus Q and here he is getting Q plus 0 into 1 minus Q. So, if Q is less than half here then what would player 1 prefer U 2 right. So, in other words if Q is less than half then in this type player 1 would prefer D 1 which is X equal to 0 and in this type he would prefer U 2 which is Y equal to 1 ok. So, if Q is less than half which means that player 1's best response is X equal to 0 and Y equal to 1. See I unlike for player 2 where I had to average over the two matrices player 1 actually knows which matrix he is in. So, there is nothing for him to average over because player 2 has only one type ok. So, that is become very simple here. So, player 1's best response now is just X equal to 0 and Y equal to 1. Now X equal to 0 and Y equal to 1 does not satisfy this equation here does not satisfy this equation ok. So, which means that Q less than half is not possible. We can similarly argue that Q. So, if Q is greater than half then what would happen the exact opposite would happen right because it is 0 into Q 1 plus 1 into 1 minus Q that type of thing. So, player 1's so then player 1's best response is X equal to 1 and Y equal to 0 which is again the same problem. So, X equal to 1 and Y equal to 0 does not satisfy this right this in this equation. So, neither of these satisfy X is equal to 1 plus 3 Y by 5 ok. Now what does this mean then? It has to be Q equal to half because we know that there is at least one equilibrium. So, which means that Q has to be equal to half ok. So, now if Q is equal to half ok then then if Q is equal to half then what you can see what happens to the payoff of the player of player 1. If Q is equal to half then both U 1 and D 1 will give him the same payoff here and U 2 and D 2 will give him the same payoff. In other words player 1 can play any X and any Y here, but then remember we were also constrained to satisfy this ok.  Now you put this together actually this gives you this gives you some kind of a region you can say you can write that out. You can see actually that this it cannot X cannot because of this because X has to be between 0 and 1 and so on and Y has to be between 0 and 1. So, you can actually take Y to be anything between 0 and 1 the X will still remain in 0 and 1, but X cannot be too large because Y also has to be between 0 and 1. So, you can what you get is that Y is between 0 and 1 and X is between one-fifth and four-fifth. So, this is there is nothing more that needs to be said these all of these points are actually equilibrium. So, X, Y, Q, X, Y, Q such that this holds and Q equals half a region actually. So, in a three it is effectively you can think of this as a like a three player thing essentially two players collectively make the other guy indifferent between his pure strategies you know that is what is happening here ok.


the courtship of the saints, how the saints met their spouses. And the book's author, Patrick O'Hearn, is with us today. I've always been fascinated with the miracle of falling in love. You know, we talk about the vocation to the priesthood and religious life, but little is mentioned about how couples fell in love. So that was just something the Holy Spirit put on my heart to dive into this topic. My grandfathers both died pretty young and I always wish that I knew their marriage story, you know, how they pursued my grandmothers. And so I think every couple, a couple should write down at some point, write down their marriage story so that their children can have it. So just in what better way than to look at the saints and how they fell in love. I think they're the ideal example for our young people to look up to.


The following contains strong language, nudity and scenes of a sexual nature. I'm so nervous about this baby shower. Josh's sister, Michaela, is a successful businesswoman. I can imagine she does not like people being late. I've known Josh's sisters for a while, but like anyone, it can be quite awkward to hang out with them without Josh around. And it's always going to be a bit nerve-wracking because I'm always going to want to see and do the right things. Sorry I'm so late. The entire room was staring at us. This is so embarrassing. Oh, yeah. But I went and got you a present, that's yours. I'll have mine. Well, it's the baby's, but I'll carry yours as well. Where've you been? I've been shopping. With Josh? With Josh. He was pushing the prams around. Josh. He was getting into it, you know. He picked one of the presents. He was honest that he was still getting into it. Are you going to try and have a baby with Josh? No. And until the end of next year, I would think about that. Yeah. I know that Makayla's opinion means a lot to Josh and I really just want that to accept us as part of the family. What's going to happen is we're getting to have a baby's bottle between the chest and then we have to drink the cocktail. With Josh's family, I did, but drinking from Makayla's cleavage. He's got it. I think I'm done. It'll meet the baby. No, yeah, it'll be next time. I think it's going to be a good looking one, you know. Yeah, I think it's going to be massive. My little brother, when he came out, he was ten pounds two. My mum had to get four stitches. Just rip the base so long you've got the length of this table. Maybe that's not the sort of thing that you say in a baby shower.


What's going on, everyone? Sam here with late sports cards. We've been 23 at Bowman Baseball Hobby, 12 box, case break number six, random team style. There's a look again at your random results. As always, you can find those on the website under the results tab, as well as a link in chat. It's good luck here, guys. We're going to do how we always do it with the Bowman hobby. We're just going to open the box, open every pack, stack them up, and then we'll just go through it. It makes it a little easier to break in general. The hobby's a little bit, I don't want to say tougher, but a little bit more difficult in terms of how the packs are structured, especially with us not chipping paper, so it makes this a little bit definitely a little bit easier. So here we go. That's pretty cool. That's awesome. Oh yeah, I'm not saying that was a bad thing or anything, but it just goes to show. Never leave the last box. You know what I mean? It's just, it's like the law at this point, you know? Never want to leave the last box. There's a Blake. A Blaper? It could be a Blaper, a Blom, one or the other. I should have you do this for me. Let's sit back and entertain the people. You do all the grunt work. Sit back, hang out, talk to Pete, talk to Lucis. You can open all the packs. It'll be your job from now on. That's with you. I'd probably get trouble if I did that. I'd probably be like, don't make them do that. It's not your... Yeah, usually expensive and dangerous rule. Very true. Very true. Very true. Very, very true. PTSD from the time case. Jeez, dude. Good Lord Elcaro. It's got a blue paper. Yulba Herrera. That's a $4.99. Wagner. Atomic. Drew Jones. Nice one there. Congrats, D-Bex. Got an Atomic base. I believe Hobby Exclusive, not numbered. Believe there? Good Lord, dude.  Manners. Never romantic. Stack of paper there. Pirata Young. A couple of Roman draft guys there. Kaminarra. Base. For the Rays. So Lunar Glow. Colton Couser. Orioles. Nice one there. Simon Juan. Jorge Burgos. Colton Carroll. Jason Dominguez. Joshua Baez. Gilbert. Gabriel Martinez. Waller. Aesteros. Puyoca Grego. Gil Watson. Tamar. Lace. Mary Ann Boyd. Samuel Munoz. Prospects. Ditas. Yafri Solano. Boyo as well as a Colton Couser. Let's do the first box here, guys. This is the way to do it for sure. I was a little suspicious on if I thought this was going to be the right way to do it, but it's for sure. Ruiz Susak. Ooh, Justin Foskew on the Bowman Scout Top 100. 2.99. There you go, Rangers. Very nice. Congrats, Rangers. Nice sit there, Justin Foskew. Kira. Lunar Glow. Juan Alonso first. The Doyers. Pona Green. Brooks Lee. Rosa. Hernandez. Michael Arroyo. Dear boy. Big Michael Arroyo guy over here next to me. Justin Crawford, first. De Los Santos. Devison, that is. And Matt Moyve-This-Woyve. Matt Mervis. Like, chrome. So funny, dude. We used to say that, so with all my college buddies, we used to think that was kind of funny doing that accent. We'd call it people nerds. You'd go, hey, it's annoyed. And one of my friends could not do it, right? He'd be like, there's a new ad. And we're like, why can't you say it right? Dude, you can't say it. Don't do it. I know. And then we'd start making fun of him, but he didn't realize it because we'd just start being like, yeah, it's a new ad. He was like really obnoxiously, and then he'd start doing it more obnoxiously too because he thought that that was the way that we were doing it. J's in for it. He's hard to upload it for me. J hits J's in for it. He's about to never want to top load again. Oh yeah. Get ready. And guys, still some spots to go in Revolution, PYC. I got two technically cases of it. You know, they're inner cases, eight box inner cases, but technically considered cases as they are also sealed. Again, teams are all on sale. That's 16 to go. Very nice. Thank you, thank you. Purple and their williams sedanio. Nice one there to 250. Congrats on that Alvin on the combo spot, their williams sedanio. Deon Jorge, Daniel Montecino, Lunar Glow first. Thank you guys again for getting these first couple of breaks filled up. I do appreciate it. Yafri Solana, Lunar Glow first. So thank you to Dylan for dropping that link. A lot of good value teams. Teams are really, really heavily on sale today too. Really heavily on sale. There are some really, really, really solid squads for like a fraction of the price. So I would definitely check that out if you're interested in some basketball. Really good squads in there still available. Pretty house, Puguerro, Robert Perez. It's Cole Young. Ooh, Jacob Berry to 3.99 on Lava. Nice one there, Marlins. Congrats on that Miami. Dohan Ke. There's Jacob at Berry. Lava Berry. It's like a Mountain Dew. New Mountain Dew Lava Berry. Stack them up at once. There's a couple of different ways of doing it for sure. Box by box. Stack them up. It's usually a little bit easier though. Cerda first. Kumar Rocker. Churio, Zack, Nido. Muñoz. Artega. Barrio. Juan Brito. My Trout Aqua Paper at 4.99, or Sky Blue Paper. I should say. Pretty angels. Nice one there. Joshua Bias. Merv the Swerve. Matt Mervis. Just got called up. Just insanity. Talk about timing for this product to come out and him getting called up like this. Somebody call you, oh, I know. It's up too, because the breakdown of it is a little bit different in comparison to Jumbo. You'll have a run of paper like that, and then you'll have chrome. You'll have your two chromes, and you'll have a run of paper, then an insert, then more paper, then your two chromes. Atomic, Henry Ramos. Nice one there for the Royals. Again, base Atomic's not numbered. And base. All right. Box two down on the box three. Plus it's, what, 24 packs in this? 12 boxes, 24 piece. So it's definitely a little bit more, obviously, than the eight of Jumbo. Hobbies fun because you get the oranges. You don't get oranges in Jumbo. Putting all these in penny sleeves. That's what I was saying. Okay, can you imagine like having to mag every single card in like a full member, like a super jumbo bum and draft break, dude? Like you'd still be doing it from like when we were doing breaks months ago. You'd still be magging every card. I forgot a way to open two packs at once. I'm pretty legit. Everything. All right. And guys, ultra high on Almanac is back as well. Oh my God. Trapio link again really quick too. Good ol' Revolution basketball down to 16. Yeah. Spots on sale. Very heavily on sale as well I should say. Teams I should say are way on sale. So definitely check that out if you guys are interested. Always a good time ripping some Revolution. It's always a fun one. Relatively inexpensive break as well to get into. Looking at about four autos per break there. Really good checklist. Some guys are on card as well. Nice. Lazaro Montez on the base auto. Grats on that one there. Mariners, Hlyn. Lazaro Montez. Nice. It is a little damaged unfortunately on the top. We'll send that empty box in wrapper. I apologize on that there. Mariners spot. Harrison Martinez. I'll get you one after this stack here. Lazaro Montez base. Orange Marcello Meyer on the Bowman Scouts top 100. Nice one there to 25 for the Red Sox. Prospect number four of 100. Lunar Glow is Kennedy Corona. Hey, what's up, Steve? Hit some green grass. Green grass or fly? I'm not even telling you actually, because you were here top one in the 10 case here. When I first saw that came out, I was like, alright dude, really green grass. And then you look at it, and it's like that is executed perfectly. Colas, Jason Dominguez. Gavin Williams. Paper first. Yosue DePaola to 250. There you go, doctors. Coral Perez, Jason Dominguez, Lunar Glow. Many Anks. Pesos, Luis Garcia. Dion Jorge. Cunha, Isaac. Corona. Jason Jones. Spencer Jones first. You're Donny De Los Santos. Oh, is that the Montez? Yeah. Alright. With those, you know. Yeah, the Bayesados, the only ones will be Mervis and Jones. You're good. That's my fault for not telling you. But yeah, I don't have to. Shandrick Martinez. Seden Rafael. 250. Seden, as I was told. This is actual name. There's a blaper in there. L.A. De La Cruz. Last stack. The last part of this stack. Drew Jones. Paper. Yosue DePaola first. Chrome for the Dodgers. Ray Soskins. Paper. Stop, Tony. All day with Tony Kay. Ladies Jordan. Atomic base. Jelloff. Adley. Rookie. Waller, Elijah Green. Paper. At least do that. One stack of paper. Go into the long spot. Yoffery Solano. And paper. Hello, Forrest. Hello, Mr. Moons. How are you doing today, sir? Hey, thanks, Tony. Taking the nuggets down to 15 to go. On our Revolution. First Revolution PY. So thank you guys. Appreciate that again. Very much, very much, very much. All on the next one. Next one going here. Good luck, guys. Some more. Yes, sir, Mercedes. Those are our paper, run of paper there. Luis Lara. Adley. Adelape. Prius. Justin Crawford first. Base. Simon. Juan. Will Watson. What's up, Chris? Freelon Bishop. For the Pirates. Thank you, Dylan. Dylan dropping you guys a link again. Down to 14 to go now. Thank you, guys. 14 to go on the first PYT. We are under half. That's Jase Bowen to 199. Junior coming on. Mark Johnson. Atomic. A little bit more suspense on the auto in this box so far, which is good. I'm always down for some suspense. Holiday. Freleon. Carnacione. Sedane. Or Sedane. Raphael. By Steros. Check up Barry first base. Cheerio. There's a Drew Jones first as well. Rojas. Future Lunar Creator. Gabriel Martinez to 199. Just... I'm just going to give him my shirt. Nice. Gabriel Martinez to 499. Refractorado. There you go, Alvin. Grats on that, buddy. Nice one there. 499. Gabriel Martinez. Refractorado. Very nice. Very, very nice. Munoz. New New Garcia. Jackson Cheerio. Lunar Globe. Peyton Graham first. The Tigers. Mejia. Berjoz. Zavala. Radio Rock. Simon Huan. Osaria. There's Luis on Helicunia. Pedro Amira. And Carlos Jorge. Paper. Roman Anthony. Gavin Cross. That's Ray Swing. Jay Savina. Howie Uli. Not Howie Ili. Howie Uli. Corbin Carroll. And Brock Jones. All right. That'll do it for that box. Pretty solid hits right there for sure. We are on to box five. So it's up there. Spinsky. All this time in the whole line. For a left. For a right. For a left. For a left. For a left. For a left. For a left. For a left. For a left. For a left. For a left. For a left. For a left. For a left. For a left. For a left. For a left. For a left. For a left. For a left. For a left. For a left. For a left. For a left. For a left. For a left. For a left. For a left. For a left. For a left. For a left. For a left. For a left. For a left. For a left. For a left. For a left. I'm Max Meyer Rookie for the Marlins. Bleak him back from Tommy John nice and healthy. He's a stud. I feel a Watson. As Lunar Glow, Robert Perez Jr. Kind of a color match there for the American. Nelson. Bruh-da. Downkill Fernandez. How you leap? Robus Martinez. Atomic, Kumar Rocker for the Rangers. Nice one there at Texas. Nice! Yanar Fernandez. Blue Lunar Crater auto to 150. Grats on that one Dodgers. Nice color match there as well. Take that, take that for show. Very nice. Laper. And guys, still at 14 to go. I'll have Dylan drop you that link again really quick. Man, he's tweeting and Facebooking. I'm going to give him a chance. Thanks, sir. Juan Chacon. Henry Davis. Purple Ray Wave to 250. Pirates. Like Martinez. Invicta Nelson-Rota. Paper. Waller. Coloss. Sedan Rafael. Denner Henderson. Trace Wing. Jackson Holliday. Josue DePaola. Harrison Rob Perez. Here's Ricardo Perez, Lunar Glow. For the Phillies. On the first. Vaughn Grissom. Cole Young. Simon Juan. Juan Alonzo. It's too early for this. It's too even for me. It's too early for this nonsense. Nonsense. Tam DePaola. That's pretty funny. I actually like that. That's pretty good. So, you guys, still plenty of good teams for Revolution PYT. Coming up a little bit later. I can tell you already. Almanac Tomorrow as well. Matt's also ripping over on the baseball channel. But Almanac Tomorrow Night with myself. Ultra High End Hit Draft. 2,200 a spot. Plenty of good stuff in there. Obviously looking at Jordan's trouts. I have no idea what else is in there. I don't even want to look at the preview pic so I can be as surprised as everybody else. Chevy Caminero. There's Blue Paper Pattern. Ivan Herrera to 125 for the Cardinals. Holiday, Gabriel Gonzalez. Francisco Alvarez. Drew Jones first. Base. Who is that? An orange shimmer I see? That is an orange shimmer I see. Someone. Let's see something big, dude. Looks like an orange shimmer auto as well if I'm not mistaken here. Come on, baby. That is Khalil Watson. And orange shimmer. Martin Gonzalez. Not an auto but still. That is 19 of 25. Martin Gonzalez. Nice one there on the orange shimmer for the Mariners. That's Mariners. More hobby exclusive. I get it. I understand why they do it. You got to have a big draw to want to open hobby. Because Jumbo is loaded. That's Louis Garcia, Lunar Glow. So it's such a big draw to making anyone want to open hobby over Jumbo. But dude, it is so sick. I wish that we saw more oranges all the time. They're so dope. I think it's the best color. I agree. And it's my favorite color too. Like in general. Really? Yeah. Being able to have a product that's not like prism football, where they're numbered to 249, so they're not as like... So it's pretty solid so far. Chase the Lauder to 399. Only three oranges so far already. No autos or anything. Two orange inserts when that orange shimmer you just saw. By the way, what's up, KJ? But yeah, some decent stuff coming out so far. Insert auto. Zach Geloff on the Lunar Glow. So Damon Heath, white speckled at 299. First auto for the Dodgers. Dodgers doing well now. A couple of hits for them. Pedro Ramirez. I need that honest. Cam Collier. Chrome first. The Reds. Chiria. Honey Nut Chiria. This is then Rafael. Dylan's actually rocking the Mischief Big Red Boots today. It's kind of wild. Odd fashion choice for sure, but hey. I picked him up yesterday. Hey, you knew you, buddy. You knew you. Interesting, but I guess I don't make the rules here. Boy, you don't like the boots? No. I don't. 14 to go, guys. Teams way on sale. Definitely take a look for sure. I would definitely highly recommend to take a look at that break at what the prices are. Teams on sale. Getting closer. I got 14 to go. I can't try. I mean, I get it. I mean, I like opening it. It's fun. It's one of the biggest baseball products that comes out every year. So it's extremely important, but I get it. It's a little different. Hobby is a little different too. Hobby is a little bit copper. Jumbo is usually a little bit more fast-paced, a little bit more exciting, but I mean, this is a super, super important product. Probably three baseball product of the year. You encapsulate all the moments together that come out all three. Chrome, draft, and regular. I disagree. I think it's the other way around. Jumbo has more of a consistent setup. That's the thing. No, no, no. Trust me. I get it. I do. 100% Kevin. I get it. Absolutely. Jumbo may have more base, but the way it's like... The way that Jumbo is set up, you can go quicker. That's the thing. Hobby is a little bit more difficult because the packs are bigger. The packs are bigger and the setup is the same all the time. You're always going to have a run of paper, one or two inserts, more paper than your Chrome. There's Kim Collier, atomic. Nice one there. Bowman issue. I like ripping Bowman a lot because I get to learn about all the prospects. That's my big thing. You get to really learn who to look out for, who the hobby is really chasing as a whole. You get to learn a lot, which is a lot of fun. A lot of times Lazaroman says, you'll see siblings or sons of former MLBers will start getting their firsts as well, which is always really cool. Especially now that players that I grew up watching are starting to have kids in the MLB, which is terrifying. I hate that. But it's cool at the same time. Please, please don't tell me if he was. Look that up, though. My god, really? Yeah. Ooh, redemption. That could be big. Come on, baby. That is Spencer Jones, orange shimmer, redemption to 25. That's big. Going to the Yanks. That is huge. Holy cow. He's got the Yanks, man. Kyle S, let's go, dude. What a way to start out today. Big time. Spencer Jones. Get that magged right away. That is massive redemption right there. Massive redemption for the best team in baseball. Good lord. Good lord. Good god.  Lunar glove. Massive, dude. Spencer Jones again. Those are not your initials, but not you. Different Kyle S. Pink paper, Oronado, two, one, Sony Bud. Surely they're not in last place in the AOEs. Ooh, Juan Brito to 15. Nice. On the first. Grats on that. They're Rockies. Juan Brito. Jackson Shuriah.  What is this called? That's the first one of those I've pulled. So after this one, I will let you know. Forrest Offhand. Do you know what that parallel is? That, like I said, that's the first one I've seen. I have no idea what they're called.  No, maybe it's black paper pattern. That's what my guess is going to be. Or some sort of strange color name. Black pattern, paper, paper pattern. Yeah, really cool, Brito. It's up, Brandon. It's Marcos Cabrera to 199. Sorry about the abs, buddy. Randy DeJesus. Lunar glove. Black pattern. That'd be my guess, yeah. There's a blaper. And brick white. Black pattern. Yeah, that'd be my guess. Again, that's the first one I've seen. So I'm assuming that's what it is called. Based on making an educated guess there. Perfect. Let's see. What do we got? What do we got? I just came in. Okay. I dropped you guys that link again to number... 27. Yeah, Teams are on sale. Definitely take a look. If you are interested in some basketball, it's very good pricing. Very, very, very, very competitive pricing on those teams. Like I said there, definitely heavily markdown, heavily on sale. So, take a look. Another orange, dude. Another orange. Gabriel Moreno. Good guy. It was like the fifth orange, this case, dude. Yeah The hell bro, she's Sarah Paguerra That is looks like auto Jason Vina nice one there for the Brewers Go brew crew that is 21 of 25 on the orange It's a second first orange auto we fold fifth orange overall unreal dude unreal Back-to-back oranges to go bro. I want Brita for that Brito rainbow here It's more. Yes, sir Mercedes Please blase Jordan Yeah, no, I mean you there's definitely when you do a case of hobby. There's like They they clearly they fill them with oranges They make sure you get your fair share of oranges in a case, which is awesome Crawford first I believe that's Carl Crawford some that makes me sick literally makes me sick I want almost Merv the swerve Matt Mervis Recently called up Matt Mervis move this wave Mashed Mervis never nervous Mervis Mervis tumbler There's a lot of names that guys have acquired over the past couple weeks in this place Jacob Barry He's not probably a fan of LSE. He hears all of his nicknames Lugo Yosue de Paula nice one there on the Lunar Glow team de Paula Jackson Holliday cross Christian Hernandez take my shirt still I'm just stop messing around Axel Sanchez the 299 white speckles Shea Ling Lears Mike your a marrow there's an Victor Justin Crawford Some crawfish in your Garcia Waller And I go Kenny Gomez there's Max Muncie atomic the A's and Paper let's keep it going here. Keep party going Keep the party going for sure. Here's again your link to My throwing that on Facebook and you get a chance to I'm gonna tweet it really quick Yeah, I'm looking for lavas galactics all the good stuff out of revolution all that good stuff Autos of course Kevin Gardner is in the product and he is on card. It's kind of like the only guy that's on car But it's cool. It's the one last night warriors right play at 30 Yeah, I know I remember I've seen that they were up 30 and like those I was thinking I was like should I watch this and then I saw they were up there Yep Dub I'm like, yeah, you better hope there was a seize dub in game two after they got smoked game one by the heat There with about a sixers right Brandon Walter Nice one there for the Red Sox There's William Lugo at 499 like Blake is like single-handedly make me dislike the Celtics more and more like more and more Jason Dominguez Lunar Glokes. I kept saying I'm like, I know they're in the Hawks You're not gonna beat him. He kept rubbing it in my face. I'm like, dude. I know I'm telling you I know that the Hawks are not gonna win that series I'm like the Hawks are gonna win two games Max True Jones first at least like at least I'm a realist when it comes to being like fans of a team Oh Edwin Arroyo God, please no to 399 for the Reds I would be like the worst possible out the worst possible outcome for me is Nick Celtics Eastern Conference finals I would be I would be livid if that's the Eastern Conference finals I am rooting so hard for heat sixers in the Eastern Conference finals God that would be like that would be like magical um Generally not what scene we usually we usually lean toward no on that one That's one of the rules we put in place. No influencing the draft or discussing card values Unfortunately Just to make it fair for everybody You know, it's way to Paula. Dude. I'm so like the Knicks have the easiest road to like the finals which sucks No, they're not The problem they're just they're clicking at the right time. We'll give them that you know, I'd help Hansa But they're not gonna beat anybody in the last Like they don't have to play the freaking box the box blew it like Yeah, if I're booting older It's also six a having your time zone Rock Jones Vincent Peruzo Atomic first. Yeah, what for I said was seen like we could pick for somebody But we're not allowed to discuss like card values or anything We can't we can't sway anybody in the direction either No, and Randall when he decides to show up, he's like he's a stud It's just a matter of if he decides to show up or not.  Thank you David down to 15. I know 13. Excuse me No paper ships in this no base paper numbered paper does Just no base paper all base chrome does all base Yeah, paper base does not ship in moment But all chrome does all numbered paper does all your hits do your inserts do Any refractors do just know Okay, race link to the next one before I forget 13 to go again teams are marked down like William just picked up the Blazers for 10 bucks off Contains some shade on sharp some dame color Shade on is a problem, dude. He he Outside of Palo has a chance to be like the best player in the class Jesus stud it's top being in Portland. I Will say that because they don't do a great job building like using free agency wisely. I Mean they haven't really been able to have successfully build around. I mean that yes and no to that one, I guess 27 now get that sold on out Kyle also be live tonight on drip. I believe Yeah, him inside. That's true. If that's true too for us. It's a good point him and Simon's run the show of dame leaves They'll probably get a ransom for dame if he leaves to if he's that they trade him He's pretty loyal dude, it's like it's like Bradley Biel. There's super loyal No, I know but I mean look at his contract 52 million a year Yeah, here's Martin Gonzalez our butler and Randall supposed to play Are they on track to play There's a gold everyone a royal it's a 50 nice one there Yeah, I mean Randall didn't play game one. I don't think Jimmy didn't play game, too So I mean that's kind of a wash for a what that's that's a wash right there Those teams both won what they should have won of Diaz de la Cruz lunar glow So once they're both healthy, we'll see who the better team is for sure It'll be exciting. That's gonna be exciting series. I'll probably watch that tonight We broke his wrist They have that team is so bad outside of not bad, but like they don't have like a true Scoring option There's your Donny De Los Santos Atomic his bands great. I'm gonna be right. I love them, but Not like a true scorer. Yeah He's a pink guy and then Lowry's old Larry could still get the job done But he's you know, he's Towards nearing the end for sure. Is that another orange swear to God another orange another orange, bro In sane, dude blue paper Marcos Cabrera to 150 for the inks Langlears Nelson rada orange cool my rocker to 25 nice one there Rangers Number six on the break. Yeah, Lord, dude Drink a berry first There's you on jalapante nice one there again Alvin with the blue jays Congrats, buddy Nice one coming your way True Jones first lunar glow Xavier Isaac first the rays There's blue paper, I've never heard of green paper. I've been a rare three ninety-nine blue Blue green same thing Corbin Carol how it's up. You see you're the next one aren't you? You see jumping into a break. I know I'd be awesome if I can get you Arizona next break Arizona since he one of the big ones The Ramirez Carlos Jorge since Chicago Cubs Rocker Munoz Ellie got him yesterday. Nice Do you buy way you got him in a in a random team? Roger green It's not bad Dodgers are pretty solid. Yeah four autos with the Dodgers is pretty good Arizona yeah, it's pretty good. It's a pretty good bowl right there zone of the Dodgers good Lord, dude Good God drop you guys this link again to Revolution 13 to go there teams are on sale very heavily marked out Time to pick up the wraps. I mean, they're not bad. You got Christian Coloco is in that There might be second-year Scotty Yeah, we just donate the paper base. Yeah, we donate it We donate it wraps aren't a terrible tick up to be honest Especially at like 17 bucks or 19 bucks, whatever they're at. It's not bad. It's definitely not bad. Oh Have to take a look see if there's any other big like that.  I am all for their Daniel Giarte. They're gonna go. I'm all for another Vancouver team Rep 80. I Don't know if it'll happen, but I'm for it for sure. I'm I'm pro Kevin air base foist Framie de Leon lunar glue Luciano Josue de Paul Colson Montgomery young kill There's on hell Jenae for the Guardians white speckler 299 nice one there congrats guardians Your Donnie de los Santos pink paper to 125 purple ray wave Marcelo Meyer to 250 for the Red Sox De La Cruz Ruiz Susak Simon one is ready to rock Noted Simon one is in fact ready to rock He is indeed ready to rock Christian Serda Guero JC young Justin Crawford first base Well as an atomic of Kenny Gomez for the Astros Merve the swerve Matt Mervis first Salute Yeah for Solano Save your Isaac first Gunner Henderson Me go blaze everyone a royal There's Colton cows are Jason and When priests there and base Good luck everybody again. I'm gonna drop you a link to the first one. We're down to 13 again Yeah teams are marked way down. I would definitely take a look if you are interested in basketball. It is very very very good pricing Very fair Thank you guys. How can I yeah, we're a lot? No, we're live. This is live. What do you mean? You'd like to break I'd say you got a time machine go back to 2016 Probably the best way to start a breaking company now It's a link to link to one of the breaks that has spots. Yeah Fox of hobby. Good luck everybody. Thanks again for getting this filled up. I've got a teal shimmer And your painter It's gonna be Montecino Tony Belanco to 125 teal shimmer or aqua shimmer. I should say this is a tops product blaze the Rojas Alvarez Zara Montez Edward Julian the old blaze Zach and Nino Riley Luis Garcia There's me got the need for me Spencer Jones first They allow cruise lunar growth lunar glow chase the water lunar glow back-to-back chase the waters Henry Davis and Braylon Bishop. There's a blue true blue Ronnie Simon nice one there for the raise to 150 Grats on that Tampa Ronnie at Simon Gabriel Gonzalez atomic J's bow Jet Williams jet the map no big first or anything. There's Jackson Cherry up prospect Card and base So quick recap everybody. Thanks again for getting this filled up Sir got all of our gold and such got gold Edwin Arroyo oranges Marcella Meyer Averson Artega Martin Gonzalez Kumar rocker unreal dude You on how a Ponte Brandon Walter was our Oman says Gabriel Martinez on hell genio to 299 as well as Damon Purple to 250 and Williams to Daniel you under Fernandez 150 Ronnie Simon 150 Justin Foskey to 99 We had orange Jason Vina 25 Brew crew and then orange shimmer Spencer Jones on The orange redemption massive card there for the angst. Thanks again for the fill guys. Next up. We got jumbo


788 here, and this is a special video for one person in particular, even though you other yahoo's are gonna see it, this is a video for Joan. So, hello Joan. Joan is a lady that I work with a lot, and Joan was interested in what I do on this YouTube channel, but she was hoping to get a video of just the funny bits, and she's not really interested in all that toy review stuff. Hey, Joan is a sophisticated 45-year-old woman. She doesn't care about G.I. Joe. This video collects some of the funny bits that I've done over the years. I hope you enjoy it. So Joan, this one's for you. I love everything about this vehicle, and when I say love, I really mean love. In fact, there's something that I've been wanting to do, and I hate to put you on the spot like this killer whale on camera, but I just have to know. Will you? This orange freak. The ice cream soldier. Look at him! I said look at him! Don't look away! Can you believe this guy? Warthog, I'm really excited about this one. Eddie's disease. Is that how you address his superior, Megat? Sorry, Sergeant. Stop saluting! You do it wrong, and it makes me sick! Sorry. How'd you get in my video? I'll ask the questions around here. I hear you do reviews of G.I. Joe toys. That's right. And you're planning to review the Sarge! Well, yes. This week I'm looking at the Warthog AIFV and Sergeant Slaughter version 3. I also hear you sometimes have negative things to say about the toys you review. Well, I have to be honest. Save it!  Listen close, Megat! If you think of anything negative to say about Sergeant Slaughter, I want you to slaughterize it! Slaughterize it! Slaughterize it! Slaughterize it! Slaughterize it! Okay, okay. I'll slaughterize it. Good vehicle all on its own. So that's it, Sarge. Was that good enough? Did I slaughterize it enough for you? I don't care about you anymore.  I'd rather talk to Mrs. Hooded Cobra Commander 788. Oh, Sergeant Slaughter. Hey! Oh, yeah! That's it. You're out of here. And that was my review of the Warthog and Sergeant Slaughter. I hope you enjoyed it. Make sure you like my video on YouTube and subscribe to my YouTube channel.  Make sure you like me on Facebook, follow me on Twitter, all the credits. Hello, everybody. Hooded Cobra Commander 788 here. It's time for another vintage GI Joe toy review. And this week, we are looking at the MP and K9, the MP and K9 law and order. This is a figure with a dog companion. As I say, this is a figure with a dog companion. James Brown. Look here, James Brown. Three things. One, you're dead. Two, I have that protective order. And three, how do all these people keep showing up in my videos? I have Sergeant Slaughter appear uninvited. Mrs. Hooded Cobra Commander wanders on to the set all the time. And now I've got James Brown. This is a closed set. I'm in the good place. At last I'm being acknowledged for all my hard work. Looks a lot like a suburban backyard. Well, hello there, big doggy. Well, hello there, big human. You're in doggy heaven. Doggy heaven? Why am I here? Did I get mis-routed? In the 90s, it was in the 80s too. So this week we're going to talk about, whoa, I just got a really tingly feeling happening to me. Where's the rest of me? Excuse me, sir. Are you Hooded Cobra Commander 788? Yes, I am, but this is a really bad time. I've got a slight problem here. I have something for you. We've had this letter since 1982 with specific instructions to deliver it to you at this very spot at this exact time. Sign here. You know, we've been taking beds at the office that you wouldn't be here. I guess I lost again. Yeah, thanks. Move two steps to the left. I kick either. It really only kicks up to about crotch level. So her real ninja action is a nut shot. You the G.I. Joe Jet that was based on the plane that was popularized by my movie Top Gun. Fooled you. It's really Hooded Cobra Commander 788. I know. I look exactly like Tom Cruise. You're not seeing double here. It's really me. Are you to work properly? This. Under this isn't working. It's broken. It's broken.  No, the long's not done yet. The wheat trimmer's broken. I'm gonna shoot a video. As Sergeant Slaughter. Hate him.   Still isn't done. I know the lawn's not done. The trimmer is broken. It was broken ten minutes ago. It hasn't magically healed itself in those ten minutes. It's broken. I'm shooting a video. I'm excited. I hope you are too. And remember until next time. Two seconds from finishing the video. I can't finish the lawn. The trimmer is broken.  It is cheap plastic. This is what I get for buying the cheap brand. It has never worked right. It is destined for the landfill where archaeologists will dig it up a hundred years from now. We're not finishing the lawn. It's an olive drab. And now the figure is naked. That's it. That's the whole shebang. I hope you enjoyed it. I certainly had a good time making it. So Audrey, what did you think of it? It stinks. Thanks for watching and Joan, I'll see you on Monday.


The determining factor of your life is quite simple. It comes down to a few things. How do you see the world? How do you interact with things? With people? With your surroundings? What is your attitude like? And in this video, I'm gonna give you a pretty fun example. And I know that everyone's gonna know what I'm talking about. And if you don't, I have a bone to pick with you. We're gonna look at the show Spongebob Squarepants. Spongebob, okay? If you're a fan of Spongebob, let me know in the comments below because I could reference that show all day long. So I wanna take a look at the character of Spongebob and we're gonna look at a few others here too. Whether or not you like his character or you find him annoying or whatever it may be, it doesn't matter. Instead, I want you to immerse yourself into being Spongebob and being in his shoes and viewing life from his eyes, okay? I think we can all agree that Spongebob, it's funny to say that, is I think that we can all agree that Spongebob is a positive, happy, just grateful person or character. He's a grateful sponge, even if it's just delusionally so. He doesn't sit around and complain or be negative or let things bring him down. Think of the episode of the hash slinging slasher. The hash slinging, the slash slinging. You know, he has to work all night for the first time the Krusty Kravistang opened for 24 hours.  I know, personally, I'd be pissed and I'd be unhappy and I'd be bitching and I'd be complaining and I'd be like, I can't believe I have to work all night long and blah, blah, blah, blah, blah, no one's gonna come to the restaurant, blah, blah, blah, like all of these negative things, at least for me and I'm sure the majority of you would spew out, right? But he goes in, he's all excited to work at night.  And then you have a Squidward, who is my personal favorite character. He is an unhappy, negative, angry character. And honestly, like in a lot of ways, I think for a lot of us, he's the most relatable character, right? He complains about everything, about everyone. He is just not a happy camper. You know, it's rare in the show that we get to see him happy and get to see him enjoying life. And why is that? Well, it's because he doesn't view life the same way as SpongeBob does. He looks at it all as that life is happening to him. The circumstances around him are controlling him. And those circumstances are people or whatever it may be, they easily sway his mood. And instead of going with the flow, he pushes back angrily, okay? Angrily at whatever that circumstance is. So again, I don't want you to look at these two characters from the outside, like we would when we're watching the show, but through their eyes, how they view the world. Step in a SpongeBob's shoes, this is so funny. Step in a Squidward's shoes. How would you rather live your life?  Let me know in the comments below. Even though from the outside watching the show, Squidward's my favorite character, if I had to choose whose life I would want to live and how I would view the world and experiences, 100%, I would be happy little SpongeBob who doesn't get mad at pretty much about anything and views life as this game, as this jungle gym, as this experience who just loves everyone and sees the best in everyone and just all around has a damn good time. So would you rather live your life the way that SpongeBob does or the way that Squidward does? And now here's the real question and I want you to be honest with yourself. Which way are you living your life right now? Are you more like Squidward or are you more like SpongeBob? Personally, I'm probably like 35% Squidward and like 65% SpongeBob, but that can change on a day to day basis. Today I'm like 90% SpongeBob, but like two days ago I was like 90% Squidward, but all in all, what percentage of SpongeBob are you and what percentage of Squidward are you? I would like to know in the comments below. So how do we switch from being Squidward dominant? I love making this video. How do we switch from being Squidward dominant to SpongeBob dominant?  You know, society, parents, whoever, they have taught us over and over again that life is about survival. You have to pay your dues and you have to work to get by and you have to do your part and play time is saved for after the work is done. But in reality, if we're living our lives through SpongeBob's eyes, it doesn't have to be that way. We can choose to not take things so seriously. We can choose to roll with the punches, go with the flow and decide to enjoy the things in life that are mundane that we initially perceived to be negative. You know, we can choose those things. You know, instead of bitching about the house being messy and having to clean the house, we can throw on some music and grab a broom and freaking dance with the broom while we're cleaning. You know, we can enjoy those things and that's what people mean by romanticizing their lives. Romanticizing, enjoying every little thing and it takes practice. You know, instead of being angry that we're stuck in traffic, enjoy the alone time because a lot of us don't get enough of it. Instead of complaining about snow, hi, hello, me. This is kind of what inspired this video was because I was driving in the gym and I was all pissed off that it was cold. We can instead bask in the beauty and the silence that it gives us, finding the enjoyment in all the things and everything. And the second way we can learn to live more through SpongeBob's eyes is to not allow outside circumstances to determine our mood, to destabilize our mood. Think about it.  And SpongeBob doesn't even let it faze him at all. He's just like, whatever. I don't care how Squidward's acting. I don't care that he's being rude to me or saying this to me. I'm not going to let that change my mood. I'm not going to let someone else or some other circumstance or something in the external world to change anything about me. No, he's living internally within his own happiness. So it doesn't matter what's going on outside of him. It only matters what's going on inside. You know, and some people might call this delusional, right? But my question is, who cares? Like who cares if the world is crumbling around you and you can still find a sliver of enjoyment or peace or whatever it may be. Why does it matter what they think of you? And you know, maybe that's a third point here, to step into SpongeBob's shoes and see the world through his eyes, not caring about what other people think so much. It doesn't matter. Okay, what matters is you. You matter and the way that you view life and in your own happiness and your peace and your fulfillment, that's what matters. So screw everyone else.  No, oh, society says you shouldn't be happy or your parents say this, your partner says this, your friends say, oh, you shouldn't be happy. Well, stop letting them Squidward your SpongeBob, okay? Don't let them. Stop letting the world and other people disturb you so greatly and stop taking everything so seriously.  So enjoy, enjoy the ride. That's what my grandpa always said. You know, it doesn't matter what happens. It's about enjoying the ride while we're here. Well, it didn't mean to get emotional there. My grandpa passed away, he was 13 years ago and we were really close. So sometimes it just hits me out of nowhere like that, but enjoy the ride. You know, the choice is yours.  If you found value in this video, it would mean the world to me if you would like it and subscribe. It doesn't cost anything and it means a lot to me and then we can hang out again next week. I love you guys so, so much and don't forget, be limitlessly yourself.