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 …

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.

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 subsequences. This questi...

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.

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.

Dec 8, 2014 · Every subsequence of xn x n has a further subsequence which converges to x x. Then the sequence xn x n converges to x x. (4 answers) Closed 8 years ago.

Feb 6, 2017 · 2 Assuming that b is indeed a subsequence of a, then p is the list of the indices of the members of a, that are in b. This is just the general definition.

Feb 13, 2024 · So any subsequence we took would be finite. But that's not possible, a subsequence should be infinite. But this assumption is not correct obviously, you can't construct such a mapping. …

Dec 11, 2019 · A subset is to a set as a subsequence is to a sequence. The only extra requirement that we impose on a subsequence is that its terms are in the same order as in the original sequence.

Nov 25, 2024 · This is from Understanding Analysis by Abbott. We have to either give an example or disprove it. A sequence that contains subsequences converging to every point in the infinite set …