Hi, I have a little question concerning contradictions : If I have a statement "A" that I want to prove, and only have the possibility for it to be True or False. After some manipulations, I arrive at some contradiction. (Here's where my question begins.) How can we know that a contradiction is enough to be sure at 100 % that a statement is not correct? Is it because in Mathematics, for a thing to be True or False, it must always be ALWAYS "working" without arriving at some contradiction ? (Mathematical ideas must always work, and not sometimes yes, sometimes no.) I just want to be sure of thinking of it in the right way, corrections would be greatly appreciated ! Thank you !