Definition:Minimal

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

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

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

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

In the context of numbers, the terms "smallest", "least" or "lowest" are often informally used for "minimal".

The term "minimum" is frequently seen instead of "minimal element".