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  2. Half-space (geometry) - Wikipedia

    en.wikipedia.org/wiki/Half-space_(geometry)

    An open half-space is either of the two open sets produced by the subtraction of a hyperplane from the affine space. A closed half-space is the union of an open half-space and the hyperplane that defines it. The open (closed) upper half-space is the half-space of all (x 1, x 2, ..., x n) such that x n > 0 (≥ 0). The open (closed) lower half ...

  3. Logarithm - Wikipedia

    en.wikipedia.org/wiki/Logarithm

    Because log(x) is the sum of the terms of the form log(1 + 2 −k) corresponding to those k for which the factor 1 + 2 −k was included in the product P, log(x) may be computed by simple addition, using a table of log(1 + 2 −k) for all k. Any base may be used for the logarithm table. [53]

  4. Mathematical game - Wikipedia

    en.wikipedia.org/wiki/Mathematical_game

    Mathematical games differ sharply from mathematical puzzles in that mathematical puzzles require specific mathematical expertise to complete, whereas mathematical games do not require a deep knowledge of mathematics to play. Often, the arithmetic core of mathematical games is not readily apparent to players untrained to note the statistical or ...

  5. Mathematical joke - Wikipedia

    en.wikipedia.org/wiki/Mathematical_joke

    The first part of this joke relies on the fact that the primitive (formed when finding the antiderivative) of the function 1/x is log().The second part is then based on the fact that the antiderivative is actually a class of functions, requiring the inclusion of a constant of integration, usually denoted as C—something which calculus students may forget.

  6. Natural logarithm - Wikipedia

    en.wikipedia.org/wiki/Natural_logarithm

    The natural logarithm of x is generally written as ln x, log e x, or sometimes, if the base e is implicit, simply log x. [2] [3] Parentheses are sometimes added for clarity, giving ln(x), log e (x), or log(x). This is done particularly when the argument to the logarithm is not a single symbol, so as to prevent ambiguity.

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  9. Supporting hyperplane - Wikipedia

    en.wikipedia.org/wiki/Supporting_hyperplane

    A convex set (in pink), a supporting hyperplane of (the dashed line), and the supporting half-space delimited by the hyperplane which contains (in light blue). In geometry , a supporting hyperplane of a set S {\displaystyle S} in Euclidean space R n {\displaystyle \mathbb {R} ^{n}} is a hyperplane that has both of the following two properties ...

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