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  2. Parity (mathematics) - Wikipedia

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

    Any two consecutive integers have opposite parity. A number (i.e., integer) expressed in the decimal numeral system is even or odd according to whether its last digit is even or odd. That is, if the last digit is 1, 3, 5, 7, or 9, then it is odd; otherwise it is even—as the last digit of any even number is 0, 2, 4, 6, or 8.

  3. Odd and Even - Wikipedia

    en.wikipedia.org/wiki/Odd_and_Even

    Odd and Even is also closely related to Royal Cotillion, which has very similar game-play but has a reserve of sixteen cards. This in turn is closely related to Contradance (Cotillion) and the single-deck game Captured Queens (Quadrille), both of which have no reserve and are entirely luck-based.

  4. Even and odd functions - Wikipedia

    en.wikipedia.org/wiki/Even_and_odd_functions

    They are named for the parity of the powers of the power functions which satisfy each condition: the function () = is even if n is an even integer, and it is odd if n is an odd integer. Even functions are those real functions whose graph is self-symmetric with respect to the y -axis, and odd functions are those whose graph is self-symmetric ...

  5. Parity of a permutation - Wikipedia

    en.wikipedia.org/wiki/Parity_of_a_permutation

    If n > 1, then there are just as many even permutations in S n as there are odd ones; [3] consequently, A n contains n!/2 permutations. (The reason is that if σ is even then (1 2)σ is odd, and if σ is odd then (1 2)σ is even, and these two maps are inverse to each other.) [3] A cycle is even if and only if its length is odd. This follows ...

  6. Odd–even rationing - Wikipedia

    en.wikipedia.org/wiki/Oddeven_rationing

    Mathematically, zero is an even number; half of the numbers in a given range end in 0, 2, 4, 6, 8 and the other half in 1, 3, 5, 7, 9, so it makes sense to include 0 with the other even digits for rationing. However, the general public is not always aware of the mathematical principle and think that zero is odd, or both even and odd, or neither.

  7. Even–odd rule - Wikipedia

    en.wikipedia.org/wiki/Evenodd_rule

    In the even–odd case, the ray is intersected by two lines, an even number; therefore P is concluded to be 'outside' the curve. By the non-zero winding rule, the ray is intersected in a clockwise direction twice, each contributing −1 to the winding score: because the total, −2, is not zero, P is concluded to be 'inside' the curve.

  8. Complex conjugate root theorem - Wikipedia

    en.wikipedia.org/wiki/Complex_conjugate_root_theorem

    But a polynomial of odd degree has an odd number of roots (fundamental theorem of algebra); Therefore some of them must be real. This requires some care in the presence of multiple roots ; but a complex root and its conjugate do have the same multiplicity (and this lemma is not hard to prove).

  9. Odd graph - Wikipedia

    en.wikipedia.org/wiki/Odd_graph

    The odd graphs have high odd girth, meaning that they contain long odd-length cycles but no short ones. However their name comes not from this property, but from the fact that each edge in the graph has an "odd man out", an element that does not participate in the two sets connected by the edge.

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