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So, this little video on numbers and number systems, not real critical to being able to understand
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pre-calculus, but some of you may not have had a little introduction like this before.
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Well, let's see. I can bring up my bad hair day here about that and talk about something like this,
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which is how many fingers do I have up? And long before there was language and number systems,
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I would say this many, or if Joe Sheeperter from ancient days wanted to tell you how many sheep he had,
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he couldn't say necessarily a number, but he could have little tokens, for example,
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each one of these pencils could represent a sheep, for example. A sheep. Of course, when he had
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10 or 15 or 20 or 30 sheep, he had to have a lot of tokens around. But he said, how many sheep do you have?
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He'd hold up all his tokens. He goes, look at all the sheep I have. Well, that idea of having a token in
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place, a physical token in place of some quantity, I got a little old, and they decided that they wanted to
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use some symbols to represent something that you could write down on a piece of paper. Of course,
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when writing implements in paper, then you could actually do that. So once we had parchment and
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writing implement, and we had a dexterity to do that, then we started writing down symbols on the
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page. So what kind of things do we do? What kind of things do we do? Well, I mean, it was pretty simple.
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What do you do? You wrote down like this. I have one sheep. I have two sheep. I have three, four.
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Well, of course, they didn't say three, four, but they just said, I had this of many sheep.
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Well, then some clever guy said, well, what if I have this of many sheep?
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It gets kind of confusing for me to tell more accurately how many sheep I have.
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So they began with ideas like this. Once I get to four sheep, of course, they didn't say four,
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they would put a line across for the next sheep, and then they would do that again when they had
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this many more sheep and this many more sheep. Okay? So then they got to this point where they
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decided that they wanted some verbal words instead of grunting and saying, oh, this many sheep,
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this many sheep, I have these many sheep. They decided that they wanted some words, and of course,
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the words that they were using are not the words that we used today. Of course,
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every language has their own word for a number. So for example, in English, this means the number one.
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It also is Uno. Okay? And then whatever language else that you want to say it in, everybody's got
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their own version of one. Everybody has their own version of this of many. In English, we call it two.
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In Spanish, they call it dose. In French, they call it Duh. Okay? So, and everybody's got their
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way of saying it, and everybody's got their own language to write it in. So great. You can
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learn the language in how to say two in every language in the known universe. That gets a little
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old because we don't want to do that. So how could we communicate? Well, we can agree on a symbol
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for this, and we can agree on a symbol for this, and we can agree on a symbol for this. And so we
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don't have to keep saying a name and writing it out in other symbols. We just want to like a
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universal symbol if we could. Okay? So what did they come up with? Well, there was a whole lot of
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different symbols out there. But the idea was this that somebody started writing down a symbol
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to represent those values. So let's see. I'm looking over here. And here's a Wikipedia page.
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It's a Wikipedia page on Arabic numerals. Guess what? Guess what? You didn't know this, but we can
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all thank the Arabs for this way of doing things. So here are the Arabic numerals. And here are
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their modifications or transmodifications into what would be a Western written language,
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something driving out of bat. Okay? So this is the way that they were originally written. And
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eventually they got a written like this. And this set of particular symbols got adopted all over
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the planet. And now it doesn't matter where you come from. If you want to talk about this a many,
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if you want to talk about this a many, let's go back here. If you want to talk about this a many,
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then
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here we go. Sorry. If you want to talk about this a many, you write this symbol. If you want to
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talk about this a many, you write this symbol. If you want to talk about this a many, you write that
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symbol. If you write this symbol for this a many. Okay? And we all know what that means. Intuitively,
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we know what that means. And okay, well, what about this symbol? What about that one? Well,
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that's like group together. So what they decided was if they could
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indicate, for example, this a many would be like one again. So I have one of these. And now I've got
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two of these groups. And now I have three of these groups. Okay? Three. Well, that would be great.
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And wouldn't it be great if I could just reuse those symbols all over again? So what if I could write
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like three and then two? What what what would that mean in this original counting system? It would
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mean three of these guys and and then two of these sticks here. Okay? So well, in English, we might
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say 32, but we'd be wrong because that's a different number. That's a different number system.
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I'm counting in groups of five. So well, we're all kind of a little prejudice. We're all a little
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prejudice. We think in groups of 10, but we don't have to think in groups of 10. We can think in
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what are groups we want. So this is actually in our system. This is 15 and two more is 17. The name
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that we give to this a many, right? The way I want that we give to this a many. How many is that?
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Here's another one. Here's another one. Okay? This a many sheep. Okay? It's really three two
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in the way I'm counting. Okay? Or 17 if we want to talk about decimal. Okay? 17 is the way we say
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this number right here. Okay? So you know what? You can count in all different kinds of
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number systems. So let me show you. So you can count in groups of two. That's generally known as
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binary. Here's a Wikipedia page on number systems. Okay? And you can count in groups of two.
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And you can count in groups of four. We just counted in groups of five. And which one did we like
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to count in groups of 10? That's our favorite. That's called the decimal system.
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Groups of 12 and heck, doh decimal 16. Wow. They don't even have 16 in here. That's a very important.
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It's called hexadecimal. Hexadecimal. And so they really missed an important one. I don't know why
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they skipped it. And here's a very important one. The base 60. Okay? Everybody knows base 60
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because that's how the clock works. We do base 60, 60 minutes, 60 seconds in a minute, 60 minutes in
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an hour. Okay? Unfortunately, it's not 60 hours in a day. So the clock counting system doesn't
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remain in base 60 just for a little bit. Okay? So that's the idea of different base systems. And we
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are so prejudiced. We are so prejudiced for the decimal system because that's what we learned
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to count in from a very young age. But we surely don't have to. Some clever people learned
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to count in base two. And now we have computers. They've realized that we could represent everything
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as an on and off base two. Yes and no. And now we have computers. So it's a good thing that people
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learned how to count in base two. Okay. So what else can I say? What else can I say here?
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The last thing that I want to say about this is that what about this zero business? So we start
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out with one, two, three, four, five. Those were counted called the counting numbers, the natural numbers.
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But what happens when we don't have anything like that example of three groups of five and
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nothing? Okay? How do I indicate nothing? When I write this down, just this one, three here,
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how do I know that I'm talking about three groups of five and not just three ones? How do I know
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where I'm talking about this or I'm talking about that? I have no idea. I have no idea. All right?
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I don't know. I could be talking about three groups of five or just three ones. So somebody came
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up with a symbol, the Arabs again, okay? Came up with this idea of nothing, a symbol to represent
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nothing. It's a very, very big deal. It's like how abstractly do you talk about no sheep, a symbol
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that represents no sheep? And they learned to put it here in a place in order to indicate
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what that three really means. If I put a three zero here, then what that saying is,
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there are three groups of these guys, okay? And then it's not this version. It's not the three
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ones here. So what happens when I do this? Oh gosh, what does that mean? There are no sticks,
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there are no groups of five, all right? But there are what? There are three groups of five groups.
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So every one of every time I do one of these, every time I do one of these five times,
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I get another group, okay? So what symbol, you know, there was no symbol that they came up with
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this one and this little stick game. But I can come up with one. What if I put a circle around it?
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What if I put a circle around one? If I put a circle around a group of five, that means there
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are five of them, okay? So when I look at this, there are no singles, there are no groups of five,
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but there are three of these five groups of five. That's what this is going to mean.
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Okay, so once again, a circle around one of these means five of these guys. So see, I've got three
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of them, all right? So that's the way we count, well, in days five, that's the way we count.
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And it works the same way in base 10, right? So what's this in base 10? It's no ones, no tens,
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and three 100s, right? So what's three hundred and twenty seven? It's seven ones, two tens,
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and three 100s. That's the way it works. Okay, that's number systems for you, number systems.