Definition, Betydelse & Synonymer | Engelska ordet INFINITELY

Definition av INFINITELY

1. avledning till adjektivet infinite

Exempel på hur man kan använda INFINITELY i en mening

• Although there are infinitely many halting probabilities, one for each (universal, see below) method of encoding programs, it is common to use the letter Ω to refer to them as if there were only one.
• Frequentist probability or frequentism is an interpretation of probability; it defines an event's probability as the limit of its relative frequency in infinitely many trials (the long-run probability).
• The existence of a complex derivative in a neighbourhood is a very strong condition: It implies that a holomorphic function is infinitely differentiable and locally equal to its own Taylor series (is analytic).
• In mathematics, a series is, roughly speaking, an addition of infinitely many terms, one after the other.
• Images of the Mandelbrot set exhibit an infinitely complicated boundary that reveals progressively ever-finer recursive detail at increasing magnifications; mathematically, the boundary of the Mandelbrot set is a fractal curve.
• It is not known whether there are any odd perfect numbers, nor whether infinitely many perfect numbers exist.
• Joseph Louis Lagrange proved that, as long as n is not a perfect square, Pell's equation has infinitely many distinct integer solutions.
• This means that any proposition whatsoever can be endlessly (infinitely) questioned, resulting in infinite regress.
• It is demonstrated that a fully occupied hotel with infinitely many rooms may still accommodate additional guests, even infinitely many of them, and this process may be repeated infinitely often.
• A transmission line of finite length (lossless or lossy) that is terminated at one end with an impedance equal to the characteristic impedance appears to the source like an infinitely long transmission line and produces no reflections.
• However, it is unknown whether there are infinitely many twin primes (the so-called twin prime conjecture) or if there is a largest pair.
• Picard's great theorem states that an analytic function with an essential singularity takes every value infinitely often, with perhaps one exception, in any neighborhood of the singularity.
• Examples of such spaces are spaces of holomorphic functions on an open domain, spaces of infinitely differentiable functions, the Schwartz spaces, and spaces of test functions and the spaces of distributions on them.
• In his first year at Polytechnique Polignac formulated his eponymous conjecture, which states that:

  For every positive integer k, there are infinitely many prime gaps of size 2k.

• This allows for treating the potential infinities of infinitely increasing sequences and infinitely decreasing series as actual infinities.
• Fourier series cannot be used to approximate arbitrary functions, because most functions have infinitely many terms in their Fourier series, and the series do not always converge.
• The partial sums of a power series are polynomials, the partial sums of the Taylor series of an analytic function are a sequence of converging polynomial approximations to the function at the center, and a converging power series can be seen as a kind of generalized polynomial with infinitely many terms.
• This is significant because one can then prove Cauchy's integral formula for these functions, and from that deduce these functions are infinitely differentiable.
• Functions of each type are infinitely differentiable, but complex analytic functions exhibit properties that do not generally hold for real analytic functions.
• It has been conjectured that there are infinitely many Sophie Germain primes, but this remains unproven.

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