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  2. Parity (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Parity_(mathematics)

    In mathematics, parity is the property of an integer of whether it is even or odd. An integer is even if it is divisible by 2, and odd if it is not. [1] For example, −4, 0, and 82 are even numbers, while −3, 5, 7, and 21 are odd numbers. The above definition of parity applies only to integer numbers, hence it cannot be applied to numbers ...

  3. Even and odd ordinals - Wikipedia

    en.wikipedia.org/wiki/Even_and_odd_ordinals

    Every limit ordinal (including 0) is even. The successor of an even ordinal is odd, and vice versa. [1] [2] Let α = λ + n, where λ is a limit ordinal and n is a natural number. The parity of α is the parity of n. [3] Let n be the finite term of the Cantor normal form of α. The parity of α is the parity of n. [4]

  4. Collatz conjecture - Wikipedia

    en.wikipedia.org/wiki/Collatz_conjecture

    The number is taken to be 'odd' or 'even' according to whether its numerator is odd or even. Then the formula for the map is exactly the same as when the domain is the integers: an 'even' such rational is divided by 2; an 'odd' such rational is multiplied by 3 and then 1 is added.

  5. Mathematics - Wikipedia

    en.wikipedia.org/wiki/Mathematics

    Mathematics is a field of study that discovers and organizes methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study ...

  6. Parity of a permutation - Wikipedia

    en.wikipedia.org/wiki/Parity_of_a_permutation

    Suppose a transposition (a b) is applied after a permutation σ. When a and b are in different cycles of σ then. and if a and b are in the same cycle of σ then. In either case, it can be seen that N( (a b)σ) = N(σ) ± 1, so the parity of N ( (a b) σ) will be different from the parity of N (σ).

  7. Parity bit - Wikipedia

    en.wikipedia.org/wiki/Parity_bit

    Accordingly, there are two variants of parity bits: even parity bit and odd parity bit. In the case of even parity, for a given set of bits, the bits whose value is 1 are counted. If that count is odd, the parity bit value is set to 1, making the total count of occurrences of 1s in the whole set (including the parity bit) an even number. If the ...

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