Continuum function

The continuum function is $\kappa\mapsto 2^\kappa$, i.e. raising 2 to the power of κ using cardinal exponentiation. Given a cardinal number, it is the cardinality of the power set of a set of the given cardinality.

See also

• Continuum hypothesis
• Cardinality of the continuum
• Beth number
• Gimel function

This set theory-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Set theory stubs Cardinal numbers Wikimedia Foundation. 2010. Игры ⚽ Нужно решить контрольную? Fabreville, Quebec Handbags and Gladrags Look at other dictionaries: Continuum mechanics — Continuum mechanics …   Wikipedia Continuum (John Mayer album) — Continuum Studio album by John Mayer Released September 9, 2006 …   Wikipedia Continuum hypothesis — This article is about the hypothesis in set theory. For the assumption in fluid mechanics, see Fluid mechanics. In mathematics, the continuum hypothesis (abbreviated CH) is a hypothesis, advanced by Georg Cantor in 1877[citation needed], about… …   Wikipedia Continuum (topology) — In the mathematical field of point set topology, a continuum (pl continua) is a nonempty compact connected metric space, or less frequently, a compact connected Hausdorff topological space. Continuum theory is the branch of topology devoted to… …   Wikipedia Continuum structure function — A continuum structure function (CSF) is defined by Baxter as a nondecreasing mapping from the unit hypercube to the unit interval. It is used by Baxter to help in the modelling of the level of performance of a system in terms of the performance… …   Wikipedia Continuum (role-playing game) — C°ntinuum roleplaying in The Yet C°ntinuum cover; illustrated by Mike Kaluta. Designer(s) Chris Adams, Dave Fooden, Barbara Manui Illustrator(s) …   Wikipedia Gimel function — In axiomatic set theory, the gimel function is the following function mapping cardinal numbers to cardinal numbers::gimelcolonkappamapstokappa^{mathrm{cf}(kappa)}where cf denotes the cofinality function; the gimel function is used for studying… …   Wikipedia Wave function — Not to be confused with the related concept of the Wave equation Some trajectories of a harmonic oscillator (a ball attached to a spring) in classical mechanics (A B) and quantum mechanics (C H). In quantum mechanics (C H), the ball has a wave… …   Wikipedia Cardinality of the continuum — In mathematics, the cardinality of the continuum, sometimes also called the power of the continuum, is the size (cardinality) of the set of real numbers mathbb R (sometimes called the continuum). The cardinality of mathbb R is often denoted by… …   Wikipedia Logistic function — A logistic function or logistic curve is the most common sigmoid curve. It modelsthe S curve of growth of some set P . The initial stage of growth is approximately exponential; then, as saturation begins, the growth slows, and at maturity, growth …   Wikipedia 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”