Bijection injection and surjection - Cardinality

In mathematics, injections, surjections and bijections are classes of functions distinguished by the manner in which arguments (input expressions from the domain) and images (output expressions from the codomain) are related or mapped to each other. A function is injective (one-to-one) if or, equivalently, if . One could also say that every element of the codomain (sometimes called range) is mapped to by at most one element (argument) of the domain; not every element of t ...

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• Bijection injection and surjection - Injection
• Bijection injection and surjection - Surjection
• Bijection injection and surjection - Bijection
• Bijection injection and surjection - Cardinality
• Bijection injection and surjection - Examples
• Bijection injection and surjection - Injective and surjective bijective
• Bijection injection and surjection - Injective and non-surjective
• Bijection injection and surjection - Non-injective and surjective
• Bijection injection and surjection - Non-injective and non-surjective
• Bijection injection and surjection - Properties
• Bijection injection and surjection - Category theory
• Bijection injection and surjection - History

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A function is bijective if it is both injective and surjective. A bijective function is a bijection (one-one correspondence). A function is bijective if and only if every possible image is mapped to by exactly one argument. This equivalent condition is formally expressed as follows. The function is bijective iff for all , there is a unique such that f(a) = b. A function f : A → B is bijective if and only if it ...

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Read more here: » Bijection injection and surjection: Encyclopedia II - Bijection injection and surjection - Bijection

It is important to specify the domain and codomain of each function since by changing these, functions which we think of as the same may have different jectivity. Bijection injection and surjection - Injective and surjective bijective. For every set A the identity function idA and thus specifically . and thus also its inverse . The exponential function and thus also its inverse the natural logarithm Bijection injection and surjection - Injective and non-s ...

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Bijection injection and surjection, Bijection injection and surjection - Injection, Bijection injection and surjection - Surjection, Bijection injection and surjection - Bijection, Bijection injection and surjection - Cardinality, Bijection injection and surjection - Examples, Bijection injection and surjection - Injective and surjective bijective, Bijection injection and surjection - Injective and non-surjective, Bijection injection and surjection - Non-injective and surjective, Bijection injection and surjection - Non-injective and non-surjective, Bijection injection and surjection - Properties, Bijection injection and surjection - Category theory, Bijection injection and surjection - History

Read more here: » Bijection injection and surjection: Encyclopedia II - Bijection injection and surjection - Examples