Now, what I want to do to take a little bit to the side and realize why this works.

If A is an axiomatic statement, it can't be the case that A and the opposite of A are both true.

What happened was that when people said, an ekename, it could sound like they were saying,

Well, that means a to the 0, right, k is 0, plus a 1 plus a squared plus a to the third plus and you could keep going plus a to the N minus 1 plus a to the N minus 2.

So this guy is going to see a and b.

So, first we have scenario A maybe I should have done all these columns in that same scenario A color.

We write that as A implies (J M) and we use this symbol to indicate an and, so that this upward facing wedge looks kind of like an A with the crossbar missing, and so you can remember A is for and where with this downward facing V symbol is the opposite of and, so that's the symbol for or.

That means if a is greater than b and a is greater than c ,

So you could add new element and if you do that it should add it to the end of a.

We know in regular mathematics, if I have 1 times a, I get a.

Or the other option we could have done is we could have added vector a.

And then 1 is obviously 1 squared.

Say A, is the ball flying towards the window? and B, is the window shattering?

And that equals well, that's just going to be a times this exact sum, right?

What is 'jjang jjang man'?

Sounds like a god

Well, we know it contains that prisoner's name, because he starts at the box that he owns.

And that's the same a as this a, right?

Alright. We noticed that all of these strings start with a lowercase a and S starts with capital A.

Well, can Mommy really come back?

So I could just drop this statement entirely.

Before I raise the question how many friends this person has,

We said, well instead of releasing the full text, we're going to release statistics about the books.

So we could say (a) plus (b), the whole square's area, is (a) plus (b) squared. ..(a) plus (b)... ...squared, and that's equal to (a) squared plus 2ab plus (b) squared.

So that's this one, where we picked this choice of coefficients.

So that numerator becomes 4 times x plus 2 times x minus 2, right? a plus b times a minus b.

Move a onto the ace of clubs.

Move a onto the ace of spades.

Move a onto the ace of hearts.

Move a onto the ace of diamonds.

It is repeated addition, a times b. Let's focus for the moment on the case where a is even.

If you'd take some value, a, and then you'd take f(a) which would put you up here. this right here would be f(a) if you would take the negative value of that, if you would take a here

But you're able to figure out pretty neat things, where you're not sure if there's enough information at first.

Here I've written out 5 candidate optimizations

And it would be extra nice if I could actually switch this multiplication around.

I equals P times A divided by T2.

What is the exponent on the a?

The second one is always true.

Just give me the answer based on plugging the means into the formula over here using the appropriate b.

And you can multiply it out, in case you're not sure.

It's just a dream, a dream

So what's a times this whole thing?

That if I multiply let me do this in this corner. a plus b times a minus b.

And we saw before that s is just our original sum.

So that's another ax.