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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).
In Latin, the sequence of tenses rule affects dependent verbs in the subjunctive mood, mainly in indirect questions, indirect commands, and purpose clauses. [4] If the main verb is in one of the non-past tenses, the subordinate verb is usually in the present or perfect subjunctive (primary sequence); if the main verb is in one of the past tenses, the subordinate verb is usually in the ...
For example, one could have an exact sequence of vector spaces and linear maps, or of modules and module homomorphisms. More generally, the notion of an exact sequence makes sense in any category with kernels and cokernels , and more specially in abelian categories , where it is widely used.
In mathematics, the Fibonacci sequence is a sequence in which each element is the sum of the two elements that precede it. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers , commonly denoted F n .
For example, the sequence 2, 6, 18, 54, ... is a geometric progression with a common ratio of 3. Similarly 10, 5, 2.5, 1.25, ... is a geometric sequence with a common ratio of 1/2. Examples of a geometric sequence are powers r k of a fixed non-zero number r, such as 2 k and 3 k. The general form of a geometric sequence is
An integer sequence is computable if there exists an algorithm that, given n, calculates a n, for all n > 0. The set of computable integer sequences is countable.The set of all integer sequences is uncountable (with cardinality equal to that of the continuum), and so not all integer sequences are computable.
For example, the sequence of powers of two (1, 2, 4, 8, ...), the basis of the binary numeral system, is a complete sequence; given any natural number, we can choose the values corresponding to the 1 bits in its binary representation and sum them to obtain that number (e.g. 37 = 100101 2 = 1 + 4 + 32). This sequence is minimal, since no value ...
1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, .. (sequence A000110 in the OEIS). Examples: We find one rhyme scheme for a one-line poem (A), two different rhyme schemes for a two-line poem (AA, AB), and five for a three-line poem: AAA, AAB, ABA, ABB, and ABC. These counts, however, include rhyme schemes in which rhyme is not employed at all ...