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an octahedral number. [2] a centered triangular number. [3] a centered square number. [4] a decagonal number. [5] the smallest number that can be expressed as a sum of two squares, with all squares greater than 1, in two ways, 85 = 9 2 + 2 2 = 7 2 + 6 2. [6] the length of the hypotenuse of four Pythagorean triangles. a Smith number in decimal. [7]
The first ordinal number that is not a natural number is expressed as ω; this is also the ordinal number of the set of natural numbers itself. The least ordinal of cardinality ℵ 0 (that is, the initial ordinal of ℵ 0 ) is ω but many well-ordered sets with cardinal number ℵ 0 have an ordinal number greater than ω .
85: Ascii85 encoding. This is the minimum number of characters needed to encode a 32 bit number into 5 printable characters in a process similar to MIME-64 encoding, since 85 5 is only slightly bigger than 2 32. Such method is 6.7% more efficient than MIME-64 which encodes a 24 bit number into 4 printable characters. 89
Natural numbers can be used for counting: one apple; two apples are one apple added to another apple, three apples are one apple added to two apples, ... The natural numbers can be used for counting (as in "there are six coins on the table"), in which case they serve as cardinal numbers. They may also be used for ordering (as in "this is the
Such a number is algebraic and can be expressed as the sum of a rational number and the square root of a rational number. Constructible number: A number representing a length that can be constructed using a compass and straightedge. Constructible numbers form a subfield of the field of algebraic numbers, and include the quadratic surds.
For every natural number n, S(n) is a natural number. That is, the natural numbers are closed under S. For all natural numbers m and n, if S(m) = S(n), then m = n. That is, S is an injection. For every natural number n, S(n) = 0 is false. That is, there is no natural number whose successor is 0.
0 is a natural number. For every natural number, there is a successor, which is also a natural number. The successors of two different natural numbers are never identical. 0 is not the successor of a natural number. If a set contains 0 and every successor then it contains every natural number. [148] [i]
An even number is an integer that is "evenly divisible" by two, that is divisible by two without remainder; an odd number is an integer that is not even. (The old-fashioned term "evenly divisible" is now almost always shortened to "divisible".) Any odd number n may be constructed by the formula n = 2k + 1, for a suitable integer k.