# 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 ?
More importantly, the availability of its different templates can suit an infinite set of topics, including business, health, and travel.
From [9,12,14], we can see that there is a 2 x 2 complex matrix whose left spectrum is an infinite set, and the left spectrum of a quaternion matrix is not a similarity invariant in general, thus the classical result ([7, Theorem 3]) about a linear map preserving eigenvalues of complex matrices is not valid for the left spectrum of a quaternion matrix.
Of this infinite set, we can dwell on three: our hunger for consolation, understanding, and love.
Sphere is defined as a finite or infinite set of trajectories having common contact (the sphere center) with some definite ratios of (infinite) oscillations numbers in order to introduce a measure for operations such as field determining integration.
As these material events unfurl, we come to perceive the succession of them as "time." The process moves us from the Absolute infinite set determined by a Platonic logic of mathematical rules, to the virtual realm of potential events, and finally events which occur in concrete fact as natural potencies relate in novel ways.
The result is an infinite set of image screw dislocations.
Let x [member of] [[GAMMA].sup.f.sub.[bar.x]], for every j [member of] N we have that [d.sub.f]({n [member of] N : [parallel][x.sub.n] - x[parallel] < 1/j}) [not equal to] 0, so let [A.sub.j] = {n [member of] N : [parallel][x.sub.n] - x[parallel] < 1/j} which is an infinite set of natural numbers and [A.sub.j+1] [subset] [A.sub.j] for every j [member of] N.
has infinite set of solutions (x, t), where x [member of] (0, [x.sub.min]].
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.
There exists an infinite set [N.sub.0] [[subset].bar] N such that, for each n [member of] [N.sub.0], there exists [t.sub.n] > 0 such that

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