Sep 24, 2017 · In mathematics, a subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements …

May 22, 2017 · I understand the definition of subsequence depends on the definition of sequence, however, I would like to have a most general or well-received definition of sequence and …

Apr 27, 2019 · A "subsequence" is an infinite selection of members from the sequence, where order is important: you have to keep selecting strictly later elements of the sequence.

Dec 14, 2011 · A subsequence of a given sequence is a sequence formed from the given sequence by deleting some of the elements without disturbing the relative positions of the …

Note that that proposition talks about a convergent sequence, and the behaviour of its subsequences, while $ (b)$ considers any sequence and it's subsequence, and the value it …

Dec 23, 2020 · If a subsequence of $ (x_n)$ diverges, it implies that, given any $\epsilon >0$, there are an infinite number of real numbers in the tail that do not lie in an $\epsilon$ …

Aug 20, 2014 · Prove that subsequence converges to limsup Ask Question Asked 12 years, 1 month ago Modified 2 years, 2 months ago

Mar 31, 2016 · How can the existence of a convergent sub-subsequence in each subsequence guarantees the convergence of sequence? For me, it looks like that in each subsequence, the …

Every subsequence has a subsequence which converges uniformly. So that isn't immediate.

Jun 9, 2013 · I know that if the sequence has a limit, it must be $L$, because the limit must equal the limit of the subsequence. But how can I prove the sequence has a limit?