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Positive integers

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The positive integers (also called the counting numbers or the whole numbers) are most often what the set of natural numbers refers to, but not always. (Many authors consider zero to be a natural number, although it was not even a number for the ancient Greeks!) The set of all positive integers (or natural numbers) may be denoted \N^* or \Z_+^*, to avoid ambiguities given that \N,~ \Z_+ or \Z^+ include 0 for many authors[1] (which is sometimes denoted by \N_0,[2] \Z_0^+ by others)[3].

A000042 Unary (so to speak, base "1") representation of natural numbers. (Tally mark representation of natural numbers, where 1 stands for a tally mark.)

{1, 11, 111, 1111, 11111, 111111, 1111111, 11111111, 111111111, 1111111111, 11111111111, 111111111111, 1111111111111, 11111111111111, 111111111111111, 1111111111111111, 11111111111111111, ...}

A000027 Denary (base 10) representation of natural numbers. Also called the whole numbers, the counting numbers or the positive integers.

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, ...}

See also


Notes

  1. For example, Steven J. Miller & Ramin Takloo-Bighash, An Invitation to Modern Number Theory, (2006) Princeton and Oxford: Princeton University Press, p. xix.
  2. Eberhard Freitag & Rolf Busam, Complex Analysis, 2nd Ed. (2009) Springer-Verlag (Universitext), pp. 519-520.
  3. Wikipedia, Natural number, http://en.wikipedia.org/wiki/Natural_number
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