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...For the ring of rational integers '''Z''' one may also take ''S'' to be a finite set of prime numbers and define an ''S''-unit to be an integer divisible only b

...gonality is not assured. However, it is always possible to orthogonalize a finite set of linearly independent set of vectors, i.e., to form linear superpositions

...t of [[real number]]s with the [[counting measure]], which assigns to each finite set of reals the number of points in the set. This measure space is not ''σ''

...either an upper or a lower bound. A ''directed set'' is one in which any finite set has an upper bound.

...The machine is always in one 'state' which is an element in a predefined, finite set of states. The head is also always in a single location on the tape (i.e.

For a finite set of data

For a finite set of data

On a finite set ''S'' of ''n'' elements, consider a function σ that defines for each

.... A related property is that rational numbers are the only numbers with [[finite set|finite]] expansions as [[continued fraction|regular continued fractions]].

If ''S'' is a [[finite set]] of numbers, then all its elements can be added together using sigma notat

...number of elements are called infinite sets. The number of elements that a finite set contains is called that set's [[cardinality]]. The concept of cardinality c

...ents in <math>A.</math> This case is called the uniform distribution (on a finite set <math>\Omega</math>), or a symmetric probability space. The uniform distrib

Any permutation of a finite set can be written as a product of permutations called ''cycles''. A cycle <mat

...finite'' if it has finitely many elements, that is if the set ''G'' is a [[finite set]].

...ive grammar is formally defined as one that is fully ''explicit''. It is a finite set of rules that can be applied to ''generate'' exactly those sentences (often

...t this in fact holds for any set (Cantor's Theorem). This is obvious for a finite set, but Cantor's ingenious proof made no reference to the set being finite; th

...there is always another prime number which is not in that set. Choose any finite set of prime numbers <math>\scriptstyle \{ p_1, p_2, p_3, \ldots, p_n \}</math> ...t. Since any finite set of prime numbers can thus be extended to a larger finite set of prime numbers, we conclude that there are infinitely many prime numbers.

# In mathematics, the number of elements in a finite set. See [[Exponent|exponent]].

...t this in fact holds for any set (Cantor's Theorem). This is obvious for a finite set, but Cantor's ingenious proof made no reference to the set being finite; th

...hed between about 1955 and 1983, which is thought to classify all of the [[finite set|finite]] [[simple group]]s into roughly 30 basic types.