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  2. Collatz conjecture - Wikipedia

    en.wikipedia.org/wiki/Collatz_conjecture

    As an illustration of this, the parity cycle (1 1 0 0 1 1 0 0) and its sub-cycle (1 1 0 0) are associated to the same fraction ⁠ 5 / 7 ⁠ when reduced to lowest terms. In this context, assuming the validity of the Collatz conjecture implies that (1 0) and (0 1) are the only parity cycles generated by positive whole numbers (1 and 2 ...

  3. Risch algorithm - Wikipedia

    en.wikipedia.org/wiki/Risch_Algorithm

    Laplace solved this problem for the case of rational functions, as he showed that the indefinite integral of a rational function is a rational function and a finite number of constant multiples of logarithms of rational functions [citation needed]. The algorithm suggested by Laplace is usually described in calculus textbooks; as a computer ...

  4. Equation solving - Wikipedia

    en.wikipedia.org/wiki/Equation_solving

    An example of using Newton–Raphson method to solve numerically the equation f(x) = 0. In mathematics, to solve an equation is to find its solutions, which are the values (numbers, functions, sets, etc.) that fulfill the condition stated by the equation, consisting generally of two expressions related by an equals sign.

  5. Elementary algebra - Wikipedia

    en.wikipedia.org/wiki/Elementary_algebra

    And, substitution allows one to derive restrictions on the possible values, or show what conditions the statement holds under. For example, taking the statement x + 1 = 0, if x is substituted with 1, this implies 1 + 1 = 2 = 0, which is false, which implies that if x + 1 = 0 then x cannot be 1.

  6. Heaviside cover-up method - Wikipedia

    en.wikipedia.org/wiki/Heaviside_cover-up_method

    Set up a partial fraction for each factor in the denominator. With this framework we apply the cover-up rule to solve for A, B, and C. D 1 is x + 1; set it equal to zero. This gives the residue for A when x = −1. Next, substitute this value of x into the fractional expression, but without D 1. Put this value down as the value of A.

  7. 5 Phrases a Child Psychologist Is Begging Parents and ...

    www.aol.com/5-phrases-child-psychologist-begging...

    In the life of your child, you easily exchange thousands of words every day, or at the very least every week. And while many of these conversations may seem normal and even fairly inconsequential ...

  8. Functional equation - Wikipedia

    en.wikipedia.org/wiki/Functional_equation

    One method of solving elementary functional equations is substitution. [citation needed] Some solutions to functional equations have exploited surjectivity, injectivity, oddness, and evenness. [citation needed] Some functional equations have been solved with the use of ansatzes, mathematical induction. [citation needed]

  9. Endangered orca vanishes from dwindling pod off Washington ...

    www.aol.com/endangered-orca-vanishes-dwindling...

    An endangered orca vanished from a dwindling whale pod off the Washington coast, a conservation group said. The missing Southern Resident killer whale, K-26, was not seen by researchers during an ...