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In mathematics, a Cauchy sequence is a sequence whose elements become arbitrarily close to each other as the sequence progresses. [1] More precisely, given any small positive distance, all excluding a finite number of elements of the sequence are less than that given distance from each other.
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called elements, or terms). The number of elements (possibly infinite) is called the length of the sequence. Unlike a set, the same elements can appear multiple times at different positions ...
In mathematics, a geometric series is a series summing the terms of an infinite geometric sequence, in which the ratio of consecutive terms is constant.
An animated gif illustrating how later terms of the Kolakoski sequence are generated by earlier terms. These self-generating properties, which remain if the sequence is written without the initial 1, mean that the Kolakoski sequence can be described as a fractal , or mathematical object that encodes its own representation on other scales. [ 1 ]
Subsequences can contain consecutive elements which were not consecutive in the original sequence. A subsequence which consists of a consecutive run of elements from the original sequence, such as ,, , from ,,,,, , is a substring. The substring is a refinement of the subsequence.
Gilbreath's conjecture is a conjecture in number theory regarding the sequences generated by applying the forward difference operator to consecutive prime numbers and leaving the results unsigned, and then repeating this process on consecutive terms in the resulting sequence, and so forth.
A post on X shows Trump ally Steve Bannon stating that President-Elect Donald Trump can actually run for a third term as President by law. Verdict: False The 22nd amendment of the U.S ...
In mathematics, an integer sequence is a sequence (i.e., an ordered list) of integers. An integer sequence may be specified explicitly by giving a formula for its n th term, or implicitly by giving a relationship between its terms.