Editing Cardinality (section)

=== Introduction ===
[[File:Aplicación 2 inyectiva sobreyectiva04.svg|thumb|250px|A one-to-one correspondence from '''N''', the set of all non-negative integers, to the set '''E''' of non-negative [[even number]]s. Although '''E''' is a proper subset of '''N''', both sets have the same cardinality.]]
The basic notions of [[Set (mathematics)|sets]] and [[Function (mathematics)|functions]] are used to develop the concept of cardinality, and technical terms therein are used throughout this article. A [[Set (mathematics)|set]] can be understood as any collection of objects, usually represented with [[curly braces]]. For example, <math>S = \{1,2,3\}</math> specifies a set, called <math>S</math>, which contains the numbers 1, 2, and 3. The symbol <math>\in</math> represents set membership, for exmaple <math>1 \in S</math> says "1 is a member of the set <math>S</math>" which is true by the definition of <math>S</math> above.

A [[Function (mathematics)|function]] is an association that maps elements of one set to the elements of another, often represented with an arrow diagram. For example, the adjacent image depicts a function which maps the set of [[natural numbers]] to the set of [[even numbers]] by multiplying by 2. If a function does not map two elements to the same place, it is called [[injective]]. If a function covers every element in the output space, it is called [[surjective]]. If a function is both injective and surjective, it is called [[bijective]]. (For further clarification, see [[Bijection, injection and surjection|''Bijection, injection and surjection'']].)