 Hi, this is Chicho. I just wanted to do a little intro for this first part of the second series of the language of mathematics. Now, as we talked about before, math is a language and a structure just like any other language. For example, if we take English, in English we have something like this called an apostrophe. What you can do is take a word and surround it by single apostrophes and you got single quotes. You can take the same word and use double quotes, double quotation marks, right? You can take the same symbol and take a word and put it in the subscript and it becomes a comma and you can use a comma in getting different types of ideas across in the sentence, right? Embedding ideas. You can take two you can take one word the same three letters and add your apostrophe and it changes the meaning between these two words, right? So the more words you know, the more symbols you know, the more grammatical rules you know in any language, the larger your vocabulary base becomes, the larger the more tools you have to get different ideas across and math works the same way. In mathematics our base number is basically, you know, the first level in mathematics is sort of writing down numbers. For example, 2 plus 3 is equal to 5, right? Now, this is your base location. Like this. In mathematics, you can get a whole bunch of different symbols surrounding your base number and one of the first places where we encounter one of these symbols or one of these grammatical, I guess, rules when it comes to mathematics is by going in the superscript, I guess, I think it's called the superscript, going above here and going into the exponent. So for example, you could have 2 to the power of 3 and this means totally something else than 2 times 3. 2 times 3 is 5. 2 to the power of 3 is 2 times 2 times 2, which is 2 times 2 is 4 times 2 is 8. Okay, which means totally something else than 2 plus 3, which is 2 times 3 is 6, sorry. And 2 plus 3 is 5, right? So depending on where you place the same two numbers and what you put between them, they have different meanings just like any other language. So what we're going to do in this first series, in this first section for the second series, is really explore the idea of exponents because that's the first place you go when you go beyond your base level. And keep in mind, there's a whole bunch of symbols. The whole bunch of symbols could be used surrounding a base number. You know, you could have a summation symbol from n is equal to 1 to infinity if you want. You could put another number here. You could do a whole kind of thing. You could, you know, there's something called a log of another number to a base of the log, okay? So all those symbols you see from pictures where you've seen mathematician or physicist standing against the blackboard and, you know, looking at all this stuff written on there, all those things are just symbols that they know what they mean. Just like quotation marks, just like comma, just like using an apostrophe to, you know, use the same letters to get a different idea across, okay? Math works the same way. So just keep this in mind when we're progressing through this whole series because we're going to start introducing functions and variables and maybe look at different types of functions and we might start using different symbols and every time we introduce a new symbol, I'm going to try to explain what they are. The first place, as I stated, the first place we're going to go to is we're going to look at exponents. Because exponents are super powerful and it's one of the first first places where you start encountering functions that are, you know, exponential functions and inverse functions and basically, exponents is a large, huge part of math 12 or mathematics in high school and they start introducing in my area anyway. You sort of look at it in grade 9, you really explore it in grade 10 and just grows from there when they start introducing functions that, you know, go through certain power or even the variables could be there, okay? So keep this in mind. We're going to go to the exponents and explore what they mean and there's different rules associated with dealing with exponents just like there were different rules associated with, you know, adding and subtracting and dividing and, you know, dealing with fractions. So exponents have their own rules when it comes to multiplying them together, adding them together. So keep all this in mind and it is mathematics is just the language and you're going to start learning more and more symbols or what the functions of some of these symbols are and when you place numbers and letters in different locations on the paper surrounding your base number here, they're going to have different meanings and they're going to tell you to do different things, okay? Now before we continue on this whole idea of math being a language and symbols in different locations mean different things on YouTube, a user posted a comment or a riddle to one of the videos from the previous series and I really liked it so thank you virus haters for posting the riddle of the puzzle. I plan on using it right now to get a point across and the riddle is now he posted a comment saying how do you solve, how do you solve the following, how do you correct the following equation and the equation is this equation is false right now because 101 subtract 102 you should have negative one because this is a bigger number than this, right? So his question was was how do you move one of these numbers so this equation becomes true, okay? 101 minus 102 is equal to 1. After looking at this for a while for a few minutes and stuff like this I should I looked at it for a while. I had no idea how to do it. I actually posted a comment saying I don't know how to do it and virus, virus hater had to haters had to post a solution for me and I loved it when I saw it. What I was doing is I was working in one plane. I was trying to move these numbers around take this one put it over here take that one put it over there and stuff like this and That's not the way you do it. I totally forgot that math is just not one-dimensional. It's multi-dimensional It's multi-planar, I guess You know, you don't have to work in this plane. You could take these numbers and move them up or down So the solution was so so brilliant so eloquent or elegant, I guess And the solution is this now if you if you want to work on this do a little pause because I'm gonna write it out right now so this gets the point across of Earlier what we talked about where different locations for different numbers do different things they have different meanings So what this ends up being is 101 minus 10 squared is equal to one and that's true Because squared in the power to this to number two in the power. We're gonna talk about this and then Just right after this video, I think but this number here means 10 times itself so 10 squared is 100 so 101 minus 100 is one Okay, and all we did was exactly what the question asked us to do was move a number now We didn't have to move this position In this, you know location. We have to move this position We have to go from down here up here and this to here has completely different meaning Then what to over here was doing? Okay, so keep this in mind math is just a language where you put things really really matters I've seen a lot of people do a lot of mistakes where you know, they keep on putting the twos the squared side They're not really putting up hope that's clear and thank you virus haters for posting this thing I really liked it totally got the point across