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In mathematics, a subsequence of a given sequence is a sequence that can be derived from the given sequence by deleting some or no elements without changing the order of the remaining elements.
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 ...
In topology and related areas of mathematics, a subnet is a generalization of the concept of subsequence to the case of nets. The analogue of "subsequence" for nets is the notion of a "subnet". The definition is not completely straightforward, but is designed to allow as many theorems about subsequences to generalize to nets as possible.
Given a sequence (), another sequence () is a subsequence of () if = for all positive integers and () is a strictly increasing sequence of natural numbers. Limits and convergence [ edit ]
In general, grouping the terms of a series creates a new series with a sequence of partial sums that is a subsequence of the partial sums of the original series. This means that if the original series converges, so does the new series after grouping: all infinite subsequences of a convergent sequence also converge to the same limit.
Which fruits are high in protein? Fruits with the most protein to help build muscle include passion fruit, jackfruit, pomegranate, apricots and more.
Last month, a juvenile gorilla was found onboard a Turkish Airlines flight from Nigeria to Thailand. Officials believe the gorilla was being trafficked for the illegal wildlife trade, finding the ...
In any metric space, a Cauchy sequence which has a convergent subsequence with limit s is itself convergent (with the same limit), since, given any real number r > 0, beyond some fixed point in the original sequence, every term of the subsequence is within distance r/2 of s, and any two terms of the original sequence are within distance r/2 of ...