Proposition that holds for both finite and infinite sets

Question

Is it generally true that if a proposition $p(n)$ holds true for any integers set of finite length $n$, then it holds true for an infinite integers set?

Answer 1

No, this is not true in general.

For example, think about one of these propositions:

• "The set is finite"
• "The sat has a maximal element"

(This is just a community wiki answer made from the comments so the question stops appearing in unanswered list.)