Question

Prove that vampires don't exist using Differential/Integral Calculus

@Jlastino stay out of this problem :P

Answer 1

@FoolForMath you're welcome to take the challenge though

Answer 2

A basic principle of first order logic is that, if a theorem follows from a list of axioms, then it follows from some finite subset of that list. This can often give nontrivial consequences. For example:

(1) If T is any true first order statement about characteristic zero fields, then there is a constant T so that T is true for fields of characteristic >N.

Proof take your list of axioms to be the standard field axioms plus, in case (1), the axiom 1+1+1+⋯+1≠0 where the sum is over p ones for each prime p.

A similar example is:

(2) If T is any true first order statement about algebraically closed fields, there is a constant N such that T is true for any field K in which every polynomial of degree ≤N has a root.

In both of these cases, it can be easier to (informally) prove a result about characteristic zero/algebraically closed fields than it is to extract the constant N.

Here is a different example. Recall that Ramsey's theorem (in a special case) says:

(3) For any positive integer N, there is an integer M such that, for any bicoloring of the complete graph on M vertices, there is a unichromatic complete subgraph on N vertices.

As I understand it, the original proof was to show

(3') For any bicoloring of the complete graph on infinitely many vertices, there is an unichromatic infinite complete subgraph.

This clearly implies

(3'') For any positive integer N, and any bicoloring of the complete graph on infinitely many vertices, there is an unichromatic complete subgraph on N vertices.

Writing (3'') formally, you wind up with an infinite sequence of axioms, saying that the graph has more than k vertices for every k. Since only finitely many of those axioms are used in the proof of (3''), we see that (3) must hold. Of course, there are now direct proofs of (3), but my understanding is that the logic theory proof came first.




I WIN

Answer 3

i dnt think that's calculus is it? i was too lazy to read the long text :P haha lol jk

Answer 4

Y u no let me solve it? King Co don't care about vampires hahaha

Answer 5

lmao. exactly why i copied.. oh wait.. i mean wrote so much, so you would just give me a medal and claim me the winner *evil laugh*

Answer 6

SCORE

Answer 7

i give you medal for being funny :P hahaha

Answer 8

But you know his explanation was wrong that vampires only wake up at full moon . Werewolves are like that :))

Answer 9

Hint: Edward Cullen does NOT exist

Answer 10

i think so...i dont know much about vampires hahaha

Answer 11

How dare you say the cullens dont exist. im going to banish you to the fiery gates of hell unless you take that back


:P