Hello guys,
I have problems understanding proofs by contradiction.
This is one of my exercises :
Give a proof by contradiction that if 2n^9 + 5n^7 - 6n^4 - n^2 - 27 = 0 where n is an integer, then n is a positive integer (n > 0)
Obviously, I have to assume that n is negative integer. What I don't know is how to proceed with the contradiction. I try to substitute n in the equation with different positive and negative integers, but it is never equal to zero
Thank you in advance for your answers.
Yes.
Yes, so . In other words, is negative.and the whole equation is going to be non-positive
Yes but what's interesting here is that 0 is non negative. As is negative, we've found the contradiction we were looking for.and Zero is not a non-positive number
Yes we do.and we make the conclusion that is positive ?