Absolute Value

If you're saying there are infinitely many primes, prove it!

Unless, of course, you are a character in Through the Looking Glass:

'When I use a word,' Humpty Dumpty said, in a rather scornful tone, 'it means just what I choose it to mean - neither more nor less.' 'The question is,' said Alice, 'whether you can make words mean so many different things.' 'The question is,' said Humpty Dumpty, 'which is to be the master - that's all.' Lewis Caroll (Charles Dodgson), Through the Looking Glass, Chapter 6 (first published in 1872).

i dont know how :sob:

You're not supposed to know; you're supposed to figure it out. But I guess it does help to know a bunch of proofs of theorems so you have a starting point of things to try.

Let's see what earthrulerr says...

i dont even know what proofs or theorem is :(

edit: off topic but omfg my crush just said yes to if he and i could walk to science together tmr i am so happy rn like

wow @bh just gave up on that message huh

I think he’s replying at the moment.

Oh. A theorem is something you prove, based on axioms. The axioms are statements that you just accept as starting points. So, to take the most famous example, Euclid's organization of geometry is based on these axioms:

  1. Two points determine a line. (That is, given any two points, there is exactly one (straight) line, no more no less, connecting them.)

  2. Two (different) lines intersect in at most one point.

  3. There is exactly one circle with a given center and radius.

  4. Any two right angles are equal.

  5. Given a line L and a point P not on the line, there is exactly one line through P parallel to L.

And from there he proves all the stuff about congruent triangles, and the angles of a triangle add up to a straight angle (180°), and so on. It's kind of amazing how much he gets out of those axioms, especially since only the fourth one says anything about sizes of things: how big is this angle, what's the distance between these two points, what's the area of this square, and so on.

(Sadly, about 150 years ago people figured out that Euclid's proofs implicitly assumed things he didn't explicitly list as axioms, e.g., for any three points on a line, one of them is between the other two. But it still takes only about 25 axioms to prove all of plane geometry rigorously.)

So, okay, a theorem is something you can prove from axioms using formal logical reasoning. For example, I'm sure you've come across the Pythagorean theorem, which says that in any right triangle the area of a square built on the longest side of the triangle is equal to the sum of the squares on the other two sides.

Does that help?

Congratulations. Is this a big deal? I mean, does "walk to science" mean walk from one room in the school to another room in the school?

For me it wouldn’t be, I walk to certain classes and electives with certain people that change. This goes from a crush to enemy.

TL;DR the bajillion posts related to math lol

Okay, time for a hint: Think about @warpedwartwars's proof about interesting numbers.

hello! a little note about the infinite amount of numbers really quick because all these prime number posts made me think about it:

okay so set theory (well, the non-self-referencing one) basically is like "hey you can do tons of things with groups of any amount with anything in them". just put all integers into a set, and pick out which is prime...

but seriously, prime numbers get further and further apart the farther you go up on the number line. assuming that integers go on forever, the amount of prime numbers is uncountable lol. it's not hard to calculate up to certain numbers, but-

HEY
WHAT ABOUT EUCLID'S THEORY THING????? that one about infinite prime numbers??

I know right.

For home room we both are in the same hallway, and science is across the school

And also yes, this helps

[edited by bh to remove personal attack on another user]

Because IT is a very annoying and demanding job (from what I've gathered, at least).

The object of the exercise is for people to figure out how to prove it, not for them to look it up in Wikipedia!

Which is why I tagged it…? I just Wikipedia’d it because I was interested in remembering a bit more- I already know what Euclid’s theorem was and what it proves, but I just didn’t remember 10,000% of it. I intended to offered it as a potential solution or helper for a solution without immediately giving out all the details.

That was a joke- sorry if I didn’t make that clear enough, haha.

They're both ³∕₂. btw that symbol isn't on its own it's ³ (superscript 3), ∕ (fraction slash), and ₂ (subscript 2).