# How to negate this statement for a proof by contradiction

I want to try and construct a proof by contradiction but am having a hard time negating this statement.

The statement that I am working with is

There are only a finite number of points accepted into the set and this finite sequence converges to a stationary point.

So I want to prove this statement but want to do it with contradiction. How do I negate this statement to start the proof?

## 1 Answer

The negation of "The subject is suchathing and behaves suchlike" is

• "Either the subject is not suchathing, or does not behave suchlike"

Either there is an infinite number of points accepted into the set, or the finite sequence does not converge to a stationary point.

• So could I say "There are only a finite number of points accepted into the set and this finite sequence does not converge to a stationary point." – RustyStatistician Dec 11 '15 at 23:16
• @RustyStatistician No. The statement in the answer is the negation of your theorem. The statement in your comment is a different statement, not equivalent to the negation of your theorem. – David K Dec 11 '15 at 23:48