Sep 24, 2017 · Intuitively, we can create a subsequence by selecting an infinite amount of random terms of this sequence, and throwing what's left away. However, it is important that if we select ai a i and aj …

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.

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 …

Sep 10, 2025 · The Bolzano-Weierstrass theorem states that every bounded sequence contains a convergent subsequence. A common construction of a subsequence that I have seen is picking …

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 …

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.

Given a sequence of real numbers, {xn}∞ n=1 {x n} n = 1 ∞, let α = α = limsup xn x n and β = β = liminf xn x n. Prove that there exists a subsequence {xnk} {x n k} that converges to α α as k → ∞ k → ∞. …

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.

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. …