24/7 Vacations Web Search

Search results

  1. Results from the 24/7 Vacations Content Network
  2. Exponentiation - Wikipedia

    en.wikipedia.org/wiki/Exponentiation

    This is because a negative number multiplied by another negative number cancels the sign, and thus gives a positive number. If n is an odd integer, then (−1) n = −1. This is because there will be a remaining −1 after removing −1 pairs. Because of this, powers of −1 are useful for expressing alternating sequences.

  3. Euler's identity - Wikipedia

    en.wikipedia.org/wiki/Euler's_identity

    The same formula applies to octonions, with a zero real part and a norm equal to 1. These formulas are a direct generalization of Euler's identity, since and are the only complex numbers with a zero real part and a norm (absolute value) equal to 1.

  4. Power series - Wikipedia

    en.wikipedia.org/wiki/Power_series

    Power series. In mathematics, a power series (in one variable) is an infinite series of the form where an represents the coefficient of the n th term and c is a constant. Power series are useful in mathematical analysis, where they arise as Taylor series of infinitely differentiable functions.

  5. Aleph number - Wikipedia

    en.wikipedia.org/wiki/Aleph_number

    Aleph-one. ℵ 1 is, by definition, the cardinality of the set of all countable ordinal numbers. This set is denoted by ω 1 (or sometimes Ω). The set ω 1 is itself an ordinal number larger than all countable ones, so it is an uncountable set. Therefore, ℵ 1 is distinct from ℵ 0. The definition of ℵ 1 implies (in ZF, Zermelo–Fraenkel ...

  6. Infinity - Wikipedia

    en.wikipedia.org/wiki/Infinity

    means that does not bound a finite area from to. means that the area under is infinite. means that the total area under is finite, and is equal to. Infinity can also be used to describe infinite series, as follows: means that the sum of the infinite series converges to some real value.

  7. Zero to the power of zero - Wikipedia

    en.wikipedia.org/wiki/Zero_to_the_power_of_zero

    Zero to the power of zero. Zero to the power of zero, denoted by 00, is a mathematical expression that is either defined as 1 or left undefined, depending on context. In algebra and combinatorics, one typically defines 00 = 1. In mathematical analysis, the expression is sometimes left undefined. Computer programming languages and software also ...

  8. Indeterminate form - Wikipedia

    en.wikipedia.org/wiki/Indeterminate_form

    A limit which unambiguously tends to infinity, for instance is not considered indeterminate. [2] The term was originally introduced by Cauchy 's student Moigno in the middle of the 19th century. The most common example of an indeterminate form is the quotient of two functions each of which converges to zero. This indeterminate form is denoted by .

  9. Natural logarithm - Wikipedia

    en.wikipedia.org/wiki/Natural_logarithm

    The natural logarithm of e itself, ln e, is 1, because e1 = e, while the natural logarithm of 1 is 0, since e0 = 1 . The natural logarithm can be defined for any positive real number a as the area under the curve y = 1/x from 1 to a[ 4] (with the area being negative when 0 < a < 1 ). The simplicity of this definition, which is matched in many ...

  1. Related searches what is the value of a number raised to the power of zero negative infinity

    exponentiation of positive numberspower series negative powers
    non zero exponentiation formula