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  2. Even and odd functions - Wikipedia

    en.wikipedia.org/wiki/Even_and_odd_functions

    The sum of two even functions is even. The sum of two odd functions is odd. The difference between two odd functions is odd. The difference between two even functions is even. The sum of an even and odd function is not even or odd, unless one of the functions is equal to zero over the given domain.

  3. Parity (mathematics) - Wikipedia

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

    Even and odd numbers have opposite parities, e.g., 22 (even number) and 13 (odd number) have opposite parities. In particular, the parity of zero is even. [2] 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 ...

  4. Fourier series - Wikipedia

    en.wikipedia.org/wiki/Fourier_series

    When the real and imaginary parts of a complex function are decomposed into their even and odd parts, there are four components, denoted below by the subscripts RE, RO, IE, and IO. And there is a one-to-one mapping between the four components of a complex time function and the four components of its complex frequency transform: [28] [29]

  5. List of types of functions - Wikipedia

    en.wikipedia.org/wiki/List_of_types_of_functions

    Even function: is symmetric with respect to the Y-axis. Formally, for each x: f (x) = f (−x). Odd function: is symmetric with respect to the origin. Formally, for each x: f (−x) = −f (x). Relative to a binary operation and an order: Subadditive function: for which the value of f (x + y) is less than or equal to f (x) + f (y).

  6. Even and odd ordinals - Wikipedia

    en.wikipedia.org/wiki/Even_and_odd_ordinals

    In mathematics, even and odd ordinals extend the concept of parity from the natural numbers to the ordinal numbers. They are useful in some transfinite induction proofs. The literature contains a few equivalent definitions of the parity of an ordinal α: Every limit ordinal (including 0) is even. The successor of an even ordinal is odd, and ...

  7. Error function - Wikipedia

    en.wikipedia.org/wiki/Error_function

    Download as PDF; Printable version ... This directly results from the fact that the integrand e −t 2 is an even function ... use the fact that erf x is an odd ...

  8. Mathematics - Wikipedia

    en.wikipedia.org/wiki/Mathematics

    A great many professional mathematicians take no interest in a definition of mathematics, or consider it undefinable. There is not even consensus on whether mathematics is an art or a science. Some just say, "mathematics is what mathematicians do". [166] [167] A common approach is to define mathematics by its object of study. [168] [169] [170 ...

  9. Greatest common divisor - Wikipedia

    en.wikipedia.org/wiki/Greatest_common_divisor

    If a is even, then divide it by two until it becomes odd. If b is even, then divide it by two until it becomes odd. Now, a and b are both odd and will remain odd until the end of the computation; While a ≠ b do If a > b, then replace a with a – b and divide the result by two until a becomes odd (as a and b are both odd, there is, at least ...

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