I have so many questions about what is really going on for proofs by contradiction.
first, what is the original questions? can that be determined from viewing this proof?
second, what is the goal of a contradiction? to make a complete reverse of the original question?
third, from reading the proof, it seems its said that that there are integers that are even for both n, then its said that n is not even, then it says because n is not even, then both n^2 and n are both not even. Is this correct?
is that what were trying to proof, that there both not even? and then must i supply work to support this.
Please help! thanks alot.
heres the proof..
proof: We will argue by contradiction.
Assume it is not the case that for every integer n, if n^2 is even then n is even
Therefore, There is an integer n s.t. n^2 is even and n is not even.
Since n is not even, n is odd by n previous Theorem. By the given result, n^2 is odd. By previous theorem
n^2 is not even --- contradiction.
--------- work goes here??? ------------
By the Method of arguing by contradiction,
For all n that exists in Z, if n^2 is even Then n is even, <end of proof>