Definition:Maximal

Let $$\left({S; \le}\right)$$ be a poset.

An element $$x \in S$$ is maximal iff:

$$x \le y \Longrightarrow x = y$$

That is, the only element of $$S$$ that $$x$$ "precedes-or-is-equal-to" is itself.

In the context of numbers, the terms "greatest" or "highest" are often informally used for "maximal".

The term "maximum" is frequently seen instead of "maximal element".