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  2. Aleph number - Wikipedia

    en.wikipedia.org/wiki/Aleph_number

    The aleph numbers differ from the infinity (∞) commonly found in algebra and calculus, in that the alephs measure the sizes of sets, while infinity is commonly defined either as an extreme limit of the real number line (applied to a function or sequence that "diverges to infinity" or "increases without bound"), or as an extreme point of the ...

  3. Extended real number line - Wikipedia

    en.wikipedia.org/wiki/Extended_real_number_line

    When dealing with both positive and negative extended real numbers, the expression / is usually left undefined, because, although it is true that for every real nonzero sequence that converges to 0, the reciprocal sequence / is eventually contained in every neighborhood of {,}, it is not true that the sequence / must itself converge to either or .

  4. 1/2 + 1/4 + 1/8 + 1/16 + ⋯ - ⋯ - Wikipedia

    en.wikipedia.org/wiki/1/2_%2B_1/4_%2B_1/8_%2B_1/...

    In mathematics, the infinite series ⁠ 1 / 2 ⁠ + ⁠ 1 / 4 ⁠ + ⁠ 1 / 8 ⁠ + ⁠ 1 / 16 ⁠ + ··· is an elementary example of a geometric series that converges absolutely. The sum of the series is 1.

  5. Limit inferior and limit superior - Wikipedia

    en.wikipedia.org/wiki/Limit_inferior_and_limit...

    In mathematical analysis, limit superior and limit inferior are important tools for studying sequences of real numbers.Since the supremum and infimum of an unbounded set of real numbers may not exist (the reals are not a complete lattice), it is convenient to consider sequences in the affinely extended real number system: we add the positive and negative infinities to the real line to give the ...

  6. 1 + 2 + 3 + 4 + ⋯ - ⋯ - Wikipedia

    en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E...

    Main page; Contents; Current events; Random article; About Wikipedia; Contact us; Pages for logged out editors learn more

  7. Particular values of the Riemann zeta function - Wikipedia

    en.wikipedia.org/wiki/Particular_values_of_the...

    The zeta function values listed below include function values at the negative even numbers (s = −2, −4, etc.), for which ζ(s) = 0 and which make up the so-called trivial zeros. The Riemann zeta function article includes a colour plot illustrating how the function varies over a continuous rectangular region of the complex plane.

  8. Arithmetic underflow - Wikipedia

    en.wikipedia.org/wiki/Arithmetic_underflow

    For integers, the term "integer underflow" typically refers to a special kind of integer overflow or integer wraparound condition whereby the result of subtraction would result in a value less than the minimum allowed for a given integer type, i.e. the ideal result was closer to negative infinity than the output type's representable value ...

  9. Operator norm - Wikipedia

    en.wikipedia.org/wiki/Operator_norm

    If = {} then the sets in the last two rows will be empty, and consequently their supremums over the set [,] will equal instead of the correct value of If the supremum is taken over the set [ 0 , ∞ ] {\displaystyle [0,\infty ]} instead, then the supremum of the empty set is 0 {\displaystyle 0} and the formulas hold for any V . {\displaystyle V.}