- #1
Demonoid
- 14
- 0
Basically I need to find a mistake in this "proof".
I claim that 0,1,2,3...are all even.
I will use induction to prove that 'n is even' for n = 0,1,2,3...
Base case is n = 0, which is true, 0 is even. I assume that the statement is true for
n = 0,1,2,3...,k and consider n = k+1. By assumption, 1 and k are both even, and thus k+1 is even as well. This means that n = 0,1,2,3... are all even.
I can't seem to find a hole in the proof. I know that 1 is not even and when we add 1 to an even number, we get an odd number. But, by assumption 1 is even, so, what do I do know ?
I claim that 0,1,2,3...are all even.
I will use induction to prove that 'n is even' for n = 0,1,2,3...
Base case is n = 0, which is true, 0 is even. I assume that the statement is true for
n = 0,1,2,3...,k and consider n = k+1. By assumption, 1 and k are both even, and thus k+1 is even as well. This means that n = 0,1,2,3... are all even.
I can't seem to find a hole in the proof. I know that 1 is not even and when we add 1 to an even number, we get an odd number. But, by assumption 1 is even, so, what do I do know ?