Negation of this mathematical expression: $x + y > z$

Question

What is the negation of this mathematic expression: $(x + y) > z$.

I want to apply negation to the whole statement i.e. $\neg \big((x + y) > z \big)$

What will be the answer?

Answer 1

If $x+y$ is not greater than $z$ it must be either less than $z$, or equal to $z$, so $x+y \leq z$

Edited (in response to OP's comment) to clarify for future readers:

The negation applies just to the logic; it has nothing to do with arithmetic. The negation of "greater than" is "not greater than". For numbers, "not greater than" is exactly the same as "less than or equal to". The fact that there's arithmetic on the left hand side is irrelevant.

Answer 2

In this situation, I sometimes start to see expressions like:

$\neg (x < y) = \neg x \ge \neg y$

... as if this is some kind of DeMorgan operation. But clearly that is a mistake: $\neg x$ has no meaning when $x$ is a number. The negation of $x < y$ is simply $x \ge y$