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An infinite sequence of real numbers (in blue). This sequence is neither increasing, decreasing, convergent, nor Cauchy. It is, however, bounded. 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).
Protein sequence interpretation: a scheme new protein to be engineered in a yeast. It is often desirable to know the unordered amino acid composition of a protein prior to attempting to find the ordered sequence, as this knowledge can be used to facilitate the discovery of errors in the sequencing process or to distinguish between ambiguous results.
A sequence ,,, … of real numbers is called a Cauchy sequence if for every positive real number , there is a positive integer N such that for all natural numbers, >, | | <, where the vertical bars denote the absolute value.
In mathematics, an exact sequence is a sequence of morphisms between objects (for example, groups, rings, modules, and, more generally, objects of an abelian category) such that the image of one morphism equals the kernel of the next.
A Cauchy sequence is a sequence whose terms ultimately become arbitrarily close together, after sufficiently many initial terms have been discarded. The notion of a Cauchy sequence is important in the study of sequences in metric spaces , and, in particular, in real analysis .
A geometric progression, also known as a geometric sequence, is a mathematical sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed number called the common ratio. For example, the sequence 2, 6, 18, 54, ... is a geometric progression with a common ratio of 3.
“Sequence is a tabletop party game requiring an abstract strategy,” comments Wyland. “It combines a card game and a board game, where players/teams try to create a sequence of five markers ...
Find recurrence relations for sequences—the form of a generating function may suggest a recurrence formula. Find relationships between sequences—if the generating functions of two sequences have a similar form, then the sequences themselves may be related. Explore the asymptotic behaviour of sequences. Prove identities involving sequences.