prepare your questions;

i'll give you a moment of time.

if you just came in, you need to look at that kid's hair.

laughter.

feel the pressure on question number ten!

whoever just came in needs to answer first.

time is flying.

we're all gonna fail this class.

another question:

how many of you did the problems?

you are all geeks.

your answers are all correct.

this is only sometimes true.

i explained this very briefly before.

please go over it again.

the distinction between so-called exercises and so-called solutions is not much of a distinction.

right now, i am reading and writing only some of the things i'm thinking.

only some of these words are true.

sometimes they say, suppose this is true?

in such cases, you have two examples of the same kind of sitaution.

suppose it is said the union of these two examples is happening. sometimes this union happens but sometimes it doesn't happen.

distant sirens.

but this example is still not equal to that example. it is very simple to see what is going on.

deception is going on.

this is always true, therefore there are conditions.

ohhhh. ohhhhh. ohhh. yea yeah.

well, I was in a rush.

this is dumb.

this is always true.

this is pure logic.

let's discuss law number 1.

law number 1 tells me these two examples are the same thing.

car horns.

a similar argument proves this law number 2.

law number 2 tells me these two examples are different.

i'm gonna show you this in a minute.

law number 2 can be proven by thinking.

i'm going to prove it to you with a little mathematical trickery.

that is what mathematicians do.

i could do this in words but i like to do it in numbers.

this is always true.

the beauty of this rule is that it is always true.

it is complicated, however. if you think about it, it is because you can never experience either of these kinds of examples in real life.

this is always true.

these rules are sometimes true.

this is simplified.

this was a rule made by people - a convention.

don't get nervous about that.

conventions happen sometimes.

here in mathematics they happen all the time.

there is another possible answer too:

this class is so boring.

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