ok, time is up. And here is the prove! Checkmate in 1!
I will use logical notation:
-> means then.
means if and only if.
means if and only if.
Argument : With Best Play for both sides Chess is a Draw
Using logical notation:
Best Play for both sides -> Chess is a draw.
Prove:
Chess is not a draw -> Not Best Play by Both sides.
1. Win for white: Black doesn't play his/her best.
2. Win for black: white doesn't play his/her best.
3. Win for white: both sides play their best.
4. Win for Black: Both sides play their best.
No. 1 and No. 2 are correct and proven immediately. So it remains to prove No. 3. and No.4. to be wrong.
If No. 3 is correct -> No. 4 is wrong. If No.4 is correct -> No. 3 is wrong. Hence No. 3 happens or No.4 happens and cannot be both at the same time. So, we only have to prove No. 3 or No. 4.
Anybody with me so far?
I am as fast as Usain Bolt. It has never been proven that I am faster than him or he is faster than me, therefore I am as fast as Usain Bolt.