finite set wikipedia - EAS
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See all on Wikipediahttps://en.wikipedia.org/wiki/Finite_setIn 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, is a finite set with five elements. The number of elements of a finite set is a natural number (possibly zero) and is
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See moreFormally, a set S is called finite if there exists a bijection
for some natural number n. The number n is the set's cardinality, denoted as |S|. The empty set { } or ∅ is considered finite, with cardinality zero....
See moreGeorg Cantor initiated his theory of sets in order to provide a mathematical treatment of infinite sets. Thus the distinction between the finite and the infinite lies at the core of set theory.
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See moreAny proper subset of a finite set S is finite and has fewer elements than S itself. As a consequence, there cannot exist a bijection between a finite set S and
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See moreIn Zermelo–Fraenkel set theory without the axiom of choice (ZF), the following conditions are all equivalent:
1. S is a finite set. That is, S can be placed into a one-to-one...
See moreIn contexts where the notion of natural number sits logically prior to any notion of set, one can define a set S as finite if S admits a
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See moreWikipedia text under CC-BY-SA license- https://simple.wikipedia.org/wiki/Finite_set
In mathematics, a finite set is a set that is not infinite. A finite set has a certain number of elements. The elements of the set can be numbered like {1, 2, ..., n } and n must either be a natural number or zero. An infinite set is a set with an unlimited number of elements. Another definition is to say a set is finite if its cardinality (the ...
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- https://en.wikipedia.org/wiki/Hereditarily_finite_set
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.
Wikipedia · Text under CC-BY-SA license- Estimated Reading Time: 3 mins
Finite set - Wikipedia
static.hlt.bme.hu/semantics/external/pages...For example, the set of all positive integers is infinite: {,,, …}. 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/Set_(mathematics)
A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets. The set with no element is the empty set; a set with a single element is a singleton.A set may have a finite number of …
- https://en.wikipedia.org/wiki/Finite_field
In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements.As with any field, a finite field is a set on which the operations of multiplication, addition, subtraction and division are defined and satisfy certain basic rules. The most common examples of finite fields are given by the integers mod p when …
