Reply to Re: I gave up to the Computers National Olimpiad
If you don't have an account, just leave the password field blank.
I have a cool new number: 15873. What should we do with it? Try multiply it by a digit(1..9), then multiply the number obtain by 7. This is quite a usefull number, right?
Now, I'm gonna prove that there are no uninteresting/unusefull natural numbers:
Let's pretend there exists uninteresting numbers. Then, we can split all the natural numbers into 2 sets. The interesting ones(A) and the uninteresting ones(B). Obviosly, the set B will have a minimum. Then, that minimum, will be the lower uninteresting number, wich suddenly becomes interesting. - contradiction. That means that there are no uninteresting numbers.
Now, I'm gonna prove that there are no uninteresting/unusefull natural numbers:
Let's pretend there exists uninteresting numbers. Then, we can split all the natural numbers into 2 sets. The interesting ones(A) and the uninteresting ones(B). Obviosly, the set B will have a minimum. Then, that minimum, will be the lower uninteresting number, wich suddenly becomes interesting. - contradiction. That means that there are no uninteresting numbers.
