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 remaining elements.

4 days ago · Find a.e. pointwisely bounded subsequence in a bounded sequence in $L^p$ Ask Question Asked yesterday Modified today

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

21 For part 1, if there were a subsequence that didn't converge to the same limit, then we could find a neighborhood around the original point such that infinitely-many subsequence terms were outside …

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 …

Dec 8, 2014 · I know that if every subsequence of a sequence converges to the same number, then the sequence converges to that same number. But I don't know if the same can be applied to …

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 converges to.