Mathematical notation for the least value a function can give

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I have a set with unknown cardinality. The cardinality can be from a number a to a number b. How can I indicate the number a (or b)?

The question in texts is: "What is the least value of n(A)" (A is a set with a few possible cardinalities) How can I properly express this in mathematical notation? I used the notation(If you call it a "notation") least of n(A)

I have seen this question: Mathematical notation for the maximum of a set of function values

The things that differ is that I need the notation to express the minimum (or max) number a function can give for a constant x, not the min (max) for a range of x

Also, the set of all possible sets isn't given and is there to be found out by the question solver. (as it implies, each solver may generate a different one)

n(A) is the cardinality of the set A

I do not have a strong mathematical background. so please avoid very confusing notations. thanks in advance