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  2. Inversion (discrete mathematics) - Wikipedia

    en.wikipedia.org/wiki/Inversion_(discrete...

    An inversion may be denoted by the pair of places (2, 4) or the pair of elements (5, 2). The inversions of this permutation using element-based notation are: (3, 1), (3, 2), (5, 1), (5, 2), and (5,4). In computer science and discrete mathematics, an inversion in a sequence is a pair of elements that are out of their natural order.

  3. Reciprocal polynomial - Wikipedia

    en.wikipedia.org/wiki/Reciprocal_polynomial

    Reciprocal polynomials have several connections with their original polynomials, including: deg p = deg p ∗ if is not 0.; p(x) = x n p ∗ (x −1). [2]α is a root of a polynomial p if and only if α −1 is a root of p ∗.

  4. Inversive geometry - Wikipedia

    en.wikipedia.org/wiki/Inversive_geometry

    This is called circle inversion or plane inversion. The inversion taking any point P (other than O ) to its image P ' also takes P ' back to P , so the result of applying the same inversion twice is the identity transformation which makes it a self-inversion (i.e. an involution).

  5. Inverse function rule - Wikipedia

    en.wikipedia.org/wiki/Inverse_function_rule

    Integrating this relationship gives = ′ (()) +.This is only useful if the integral exists. In particular we need ′ to be non-zero across the range of integration. It follows that a function that has a continuous derivative has an inverse in a neighbourhood of every point where the derivative is non-zero.

  6. Set inversion - Wikipedia

    en.wikipedia.org/wiki/Set_inversion

    In mathematics, set inversion is the problem of characterizing the preimage X of a set Y by a function f, i.e., X = f −1 (Y ) = {x ∈ R n | f(x) ∈ Y }. It can also be viewed as the problem of describing the solution set of the quantified constraint " Y ( f ( x ))", where Y ( y ) is a constraint, e.g. an inequality , describing the set Y .

  7. Here's How Much Every State Will Spend Per Child This Christmas

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    Take a look at every state ranked by how much each parent is going to spend on each kid this holiday season.

  8. Idaho abortion trafficking law partly revived by US appeals court

    www.aol.com/news/idaho-abortion-trafficking-law...

    By Brendan Pierson (Reuters) -Idaho can enforce a first-of-its-kind "abortion trafficking" law against those who harbor or transport a minor to get an abortion out of state without parental ...

  9. What is impoundment? How Trump thinks he can control spending ...

    www.aol.com/impoundment-trump-thinks-control...

    A version of this story appeared in CNN’s What Matters newsletter. To get it in your inbox, sign up for free here. “Impoundment” is another word that Americans may need to learn in the ...

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