http://www.bing.com:80/search?q=Subsequence+Maths+ExamplesSearch resultshttp://www.bing.com:80/s/a/rsslogo.gifhttp://www.bing.com:80/search?q=Subsequence+Maths+ExamplesCopyright © 2026 Microsoft. All rights reserved. These XML results may not be used, reproduced or transmitted in any manner or for any purpose other than rendering Bing results within an RSS aggregator for your personal, non-commercial use. Any other use of these results requires express written permission from Microsoft Corporation. By accessing this web page or using these results in any manner whatsoever, you agree to be bound by the foregoing restrictions.https://math.stackexchange.com/questions/2442042/what-is-a-subsequence-in-calculusIn 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 Formally, a subsequence of the sequence $ (a_n)_ {n \in \mathbb {N}}$ is any sequence of the form $ (a_ {n_k})_ {k \in \mathbb {N}}$ where $ (n_k)_ {k \in \mathbb {N}}$ is a strictly increasing sequence of positive integers. Hence ...Wed, 22 Apr 2026 07:02:00 GMThttps://math.stackexchange.com/questions/3204163/the-definition-of-a-subsequenceA "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.Fri, 17 Apr 2026 17:31:00 GMThttps://math.stackexchange.com/questions/2292690/definition-of-subsequencesI 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...Wed, 22 Apr 2026 20:10:00 GMThttps://math.stackexchange.com/questions/91384/notation-for-a-subsequence-of-a-sequenceA 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.Sun, 19 Apr 2026 08:17:00 GMThttps://math.stackexchange.com/questions/5095339/what-constitutes-a-subsequenceThe Bolzano-Weierstrass theorem states that every bounded sequence contains a convergent subsequence. A common construction of a subsequence that I have seen is picking terms from the original sequ...Mon, 20 Apr 2026 01:14:00 GMThttps://math.stackexchange.com/questions/5003021/sequence-and-subsequenceThis 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 $\\{1,1/2,1/3,1/...Tue, 21 Apr 2026 02:03:00 GMThttps://math.stackexchange.com/questions/205079/convergent-subsequencesNote 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.Wed, 22 Apr 2026 04:17:00 GMThttps://math.stackexchange.com/questions/673132/is-a-sequence-a-subsequence-of-itselfDepending on your definition of sequence and subsequence, not every sequence has a proper sequence. Let us assume that a sequence means an infinite sequence (that is a function from $\mathbb {N}$ to $\mathbb {R}$) and a subsequence means a sequence generated from another sequence by deleting zero or more elements.Thu, 23 Apr 2026 17:59:00 GMThttps://math.stackexchange.com/questions/213285/prove-if-a-sequence-converges-then-every-subsequence-converges-to-the-same-lim21 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 the neighborhood. Then infinitely many sequence terms are outside the neighborhood, and so the sequence can't converge to the original point.Thu, 23 Apr 2026 12:09:00 GMThttps://math.stackexchange.com/questions/3472678/the-definition-of-a-subsequenceA 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.Mon, 06 Apr 2026 01:16:00 GMT