In Arrow-Hahn's textbook 'General competitive Analysis', there is a sentence ‘ a bounded function f(t) where t>=0 has a limit point’.
Please teach me the definition of a limit point of a function.
First I supposed that the usual definition of a limit point ' a point A is a limit point of subset S if and only if the any ε-neighborhood of A contains some points of S different from A could be applied when {f(t),t>=0} is regarded as a subset S.
But this definition implies that any point belonging to {f(t) t>=0} is a limit point of f(t) when f(t) is a continuous function and I found this definition faces some difficulties in the explanation of stability analysis.
So I think another definition ' a point A is a limit point of f(t) if and only if there is a increasing sequence {t1,t2,t3,…} ti→∞ such that f(ti)→A'
I would like to know whether this definition is right and a more formal definition if any.
Best regards