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What (who) is finite sets - definition

SET THAT HAS A FINITE NUMBER OF ELEMENTS

K-subsets; N-set; Finite Set; K-subset; Finitely many; N-subset; Finite sets; Kuratowski-finite; Kuratowski finiteness; Kuratowski finite; Two-set; Tarski-finite set; Kuratowski-finite set; Tarski finiteness

Finite set

In mathematics, particularly set theory, a finite set is a set that has a [number of element]s. Informally, a finite set is a set which one could in principle count and finish counting.

https://en.wikipedia.org/wiki/Finite_set

Hereditarily finite set

FINITE SETS WHOSE ELEMENTS ARE ALL HEREDITARILY FINITE SETS

Hereditarily finite; Hereditarily finite sets; Pure finite set; Ackermann coding; Ackermann encoding

In mathematics and set theory, hereditarily finite sets are defined as finite sets whose elements are all hereditarily finite sets. In other words, the set itself is finite, and all of its elements are finite sets, recursively all the way down to the empty set.

https://en.wikipedia.org/wiki/Hereditarily_finite_set

Finite morphism

Finite map (algebraic geometry); Finite type scheme

In algebraic geometry, a finite morphism between two affine varieties X, Y is a dense regular map which induces isomorphic inclusion k\left[Y\right]\hookrightarrow k\left[X\right] between their coordinate rings, such that k\left[X\right] is integral over k\left[Y\right]. This definition can be extended to the quasi-projective varieties, such that a regular map f\colon X\to Y between quasiprojective varieties is finite if any point like y\in Y has an affine neighbourhood V such that U=f^{-1}(V) is affine and f\colon U\to V is a finite map (in view of the previous definition, because it is between affine varieties).

https://en.wikipedia.org/wiki/Finite_morphism

Wikipedia

Finite set

In mathematics, particularly set theory, a finite set is a set that has a finite number of elements. Informally, a finite set is a set which one could in principle count and finish counting. For example,

\{2,4,6,8,10\}

is a finite set with five elements. The number of elements of a finite set is a natural number (possibly zero) and is called the cardinality (or the cardinal number) of the set. A set that is not a finite set is called an infinite set. For example, the set of all positive integers is infinite:

\{1,2,3,\ldots \}.

Finite sets are particularly important in combinatorics, the mathematical study of counting. Many arguments involving finite sets rely on the pigeonhole principle, which states that there cannot exist an injective function from a larger finite set to a smaller finite set.

https://en.wikipedia.org/wiki/Finite set