What does minimum mean in math terms?

Answer 1

less than

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Not quite - it does not say whether the minimum is "less than" something or something is "less than" the minimum!

The minimum of a finite set of numbers is the smallest value in the set. It is a member of the set which is less than (or equal to) all members of the set.

If you want a bit more, read on, otherwise the above will be fine.

For an infinite set it is the largest number, which may or may not belong to the set, which is less than or equal to all members of the set.

Why the distinction?

Think of the set of positive integers. What is the minimum? Easy, it is 1. It is a member of the set and is less than or equal to all members of the set.

So far so good. Now think of all positive fractions. The minimum? It is 0, but that is not a member of the set. On the other hand, no number bigger than 0 can be the minimum, because half that number will be a positive fraction but will be smaller than the minimum - ooops!

Sometimes the minimum will be a member of the set, sometimes not - it depends on how the set is defined.

Actually, the definition of the minimum is very, very important, because it forms the basis of Richard Dedekind's definition of numbers and all of number theory follows from it.