how to use union and intersection symbol to denote the limit

Asked Oct 06 '21 at 18:29

Active Oct 06 '21 at 19:14

Viewed 74 times

For any $x \in X$, $f_n(x) \to \infty$ as $n \to \infty$.

Is this equivalent to saying $\cap_{K=1}^{\infty} \cup_{N=1}^{\infty} \cap_{n=N}^{\infty} \{x: f_n(x)\geq K\}$? Why?

My understanding: for any a positive integer K, we can find N, such that when n>N, then $f_n(x)>K$?

edited Oct 06 '21 at 19:14

asked Oct 06 '21 at 18:29

Mariana

And what are your thoughts and attempts to solve this? – Conifold Oct 06 '21 at 18:59
What you have is some subset of $X$. At a bare minimum you'd need to make a statement about this set in order for it to be equivalent to the statement you made about the limits of $f_n(x)$. – Jamie Radcliffe Oct 06 '21 at 19:06
@JamieRadcliffe I made a statement. – Mariana Oct 07 '21 at 10:10

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