Proof by Contradiction

Ben discusses proof by contradiction and goes through some examples.

[leftytaber]

If you want to prove "If P then Q" by contradiction, you assume the negation of "If P then Q", which is NOT "If P then not Q" as you have written. For example the negation of "If 0 = 1 then 2 = 3" is NOT "if 0 = 1 then 2 does not equal 3". After all, they are both true! Another example: "If x > 5 then x is not 2". The negation is not "if x>5 then x=2". The negation is "There is an x such that x>5 and x =2".

[theawsomist]

Well.. twas good enough for me XD if you're studying proofs by contradiction, it is assumed that you already know the basic know how of the Discrete Mathematics.

[dodgecrockett]

I'm sorry but this is really sad. You blandly state at the outset that “If P then Q”. Most newcomers to mathematics think that letters of the alphabet represent numbers. Could you not be bothered to enlighten us to the fact that “P” and “Q” represent statements instead of numbers? Throughout the course of your “presentation”, you made absolutely no effort to demonstrate how those cryptic conditional statements apply to the theorems that you attempted to “prove”. At the very least, you could have phrased these theorems so that they syntactically paralleled "If P then Q". There's a circular irony at work here: in order to understand your presentation, you'd have to already be familiar with proof by contradiction, in which case, there's no need to view it in the first place. By the way, your demeanor suggests that your goal was to just get this thing over with. If you’re going to make any more of these videos, take a little pride in your work.