Expert: Sherry Wallin - 2/20/2011

Question
I'm learning(trying to)how to do proofs.
Can you work this example out for me, the book isn't much help.
Given: x and y are real numbers x>=0 and y>=0
Prove: if x+y=0 then x=y=0

Answer
Paula~

Proofs are difficult and only come over a long time of reviewing, reading, and deciphering other peoples proofs. I can give you a proof and I will, but I think you will say, well duh, when you finally understand what I did. I did not know this proof but everything moves logically from one step to another, so here goes:

You are given some important pieces of information. One is that both x and y >=0, in other words non negative. You also get to assume that x + y = 0 so starting with x + y = 0 algebraically you get
x = -y, but y>=0 so -y <= 0. Aha! y is not < 0 so y has to be 0 and if y = 0, then x + 0 = 0 forcing x = 0 also.


Happy proofing!
Math Prof