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  2. Sequence - Wikipedia

    en.wikipedia.org/wiki/Sequence

    which is to say, infinite sequences of elements indexed by natural numbers. A sequence may start with an index different from 1 or 0. For example, the sequence defined by x n = 1/log(n) would be defined only for n ≥ 2.

  3. List of integer sequences - Wikipedia

    en.wikipedia.org/wiki/List_of_integer_sequences

    A natural number n that is equal to the sum of all or some of its ... At each stage an alternating sequence of 1s and 0s is inserted between the terms of the previous ...

  4. Natural Sequence Farming - Wikipedia

    en.wikipedia.org/wiki/Natural_Sequence_Farming

    An example of salinity, areas surrounding Dumbleyung Lake have become unsuitable for grazing.. Natural Sequence Farming (NSF) is a method of landscape regeneration devised by the Australian farmer, Peter Andrews, in the 1970s.

  5. Collatz conjecture - Wikipedia

    en.wikipedia.org/wiki/Collatz_conjecture

    The parity sequence is the same as the sequence of operations. Using this form for f(n), it can be shown that the parity sequences for two numbers m and n will agree in the first k terms if and only if m and n are equivalent modulo 2 k. This implies that every number is uniquely identified by its parity sequence, and moreover that if there are ...

  6. Exact sequence - Wikipedia

    en.wikipedia.org/wiki/Exact_sequence

    If we take a series of short exact sequences linked by chain complexes (that is, a short exact sequence of chain complexes, or from another point of view, a chain complex of short exact sequences), then we can derive from this a long exact sequence (that is, an exact sequence indexed by the natural numbers) on homology by application of the zig ...

  7. Goodstein's theorem - Wikipedia

    en.wikipedia.org/wiki/Goodstein's_theorem

    The Goodstein sequence of a number m is a sequence of natural numbers. The first element in the sequence G m {\displaystyle G_{m}} is m itself. To get the second, G m ( 2 ) {\displaystyle G_{m}(2)} , write m in hereditary base-2 notation, change all the 2s to 3s, and then subtract 1 from the result.

  8. Natural sequence - Wikipedia

    en.wikipedia.org/wiki/Natural_sequence

    Natural sequence may refer to: Natural sequence of tenses, in grammar; Natural Sequence Farming; See also. Natural number; Sequence (disambiguation)

  9. Complete sequence - Wikipedia

    en.wikipedia.org/wiki/Complete_sequence

    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 ...