infinite set

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infinite set

[′in·fə·nət ′set]
(mathematics)
A set with more elements than any fixed integer; such a set can be put into a one to one correspondence with a proper subset of itself.

infinite set

(mathematics)
A set with an infinite number of elements. There are several possible definitions, e.g.

(i) ("Dedekind infinite") A set X is infinite if there exists a bijection (one-to-one mapping) between X and some proper subset of X.

(ii) A set X is infinite if there exists an injection from N (the set of natural numbers) to X.

In the presence of the Axiom of Choice all such definitions are equivalent.
References in periodicals archive ?
The self-directed IRA offers an almost infinite set of investment options, and as the owner, you determine where and how your money is invested.
The advent of the personal cloud means that every user can now have a scalable and nearly infinite set of resources available for whatever they need to do.
The advent of the cloud means that every user can now have a scalable and nearly infinite set of resources available for whatever they need to do.
By repeatedly applying the power set operation to the original, infinite set, we thus obtain an apparently boundless hierarchy of larger infinite sets, whose relations of size or cardinality can then be discussed and compared.
The hotel's Pan Asian specialty restaurant is offering a special infinite set meal menu on December 24 and 25, 2011.
Steve Puetz, a mathematician and statistician, wrote The Unified Cycle Theory (2009), a landmark book announcing the discovery of a seemingly infinite set of cycles, now dubbed the UWS cycles.
Consider a world that contains an infinite set of locations each having some finite non-zero positive value k, and another infinite set of locations each having a finite negative value -k.
Multiair has a potentially infinite set of range of settings - so engine flexibility, responsiveness, fuel efficiency and power can all be optimised at every engine speed and throttle setting.
Topics include many inspired by the Atlas of Lie Groups Project, such as the omega regular unitary dual of the metaplectic group of Rank 2, a resolvant trace formula for the BTZ black hole with conical singularity, the geometry of coisotropic submanifolds of Poisson manifolds, ultrafilters on the collection of finite subsets of an infinite set, the scope and success of the atlas of Lie groups and representations, maximal tori of reductive centralizers of nilpotents in exceptional complex symmetric spaces, and a survey of participants in the Council for African American Researchers in the Mathematical Sciences.
McLennan offers the example of an auction in which each bidder can bid any amount--mathematically, an infinite set of numbers.
Infinite set points and flexible rule sets help accommodate tenants' needs without excessively overheating the building.

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