/sci/ - Science & Math

>>7727910
>>7727935
It's an obvious humour thread. Come on, this stuff is hilarious

>>7539542

I have created a very weird function and I want people who know mathematical logic to check my thinking.

Gödel numbering allows us to number proofs. Define F_n to be the set of all functions from N->N which have a proof of Gödel number less than n which has the conclusion that the function exists. Note that F_n is a finite set, and that for each f in F_n, f(n) is defined. Thus there is a maximum f(n) in F_n. Define the function w in the following manner: w(n) = max (F_n(n)) + 1. Suppose w could be proved to exist. Then there would be some Gödel number, a, that expressed that proof. But then w would be in F_a and w(a) = max (F_a(a)) + 1 > w(a) + 1 and so 0 > 1, a contradiction. So w cannot be proven to exist. But w(n) can be shown to exist for all n, because F_n exists for all n, and max F_n(n) exists for all n.

Have I made a mistake somewhere, or is all this kosher? Is the existence of w independent of arithmetic?