Editing Surjective function (section)

== Gallery ==
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|Image:Surjection.svg|A non-injective '''surjective''' function (surjection, not a bijection)
|Image:Bijection.svg|An injective '''surjective''' function (bijection)
|Image:Injection.svg|An injective non-surjective function (injection, not a bijection)
|Image:Not-Injection-Surjection.svg|A non-injective non-surjective function (neither a bijection)
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File:Surjective composition.svg|Surjective composition: the first function need not be surjective.
File:Non-surjective function2.svg|alt=|'''Non-surjective functions''' in the Cartesian plane. Although some parts of the function are surjective, where elements ''y'' in ''Y'' do have a value ''x'' in ''X'' such that ''y'' = ''f''(''x''), some parts are not. '''Left:''' There is ''y''<sub>0</sub> in ''Y'', but there is no ''x''<sub>0</sub> in ''X'' such that ''y''<sub>0</sub> = ''f''(''x''<sub>0</sub>). '''Right:''' There are ''y''<sub>1</sub>, ''y''<sub>2</sub> and ''y''<sub>3</sub> in ''Y'', but there are no ''x''<sub>1</sub>, ''x''<sub>2</sub>, and ''x''<sub>3</sub> in ''X'' such that ''y''<sub>1</sub> = ''f''(''x''<sub>1</sub>), ''y''<sub>2</sub> = ''f''(''x''<sub>2</sub>), and ''y''<sub>3</sub> = ''f''(''x''<sub>3</sub>).
File:Surjective function.svg|alt=|Interpretation for '''surjective functions''' in the Cartesian plane, defined by the mapping ''f'' : ''X'' → ''Y'', where ''y'' = ''f''(''x''), ''X'' = domain of function, ''Y'' = range of function. Every element in the range is mapped onto from an element in the domain, by the rule ''f''. There may be a number of domain elements which map to the same range element. That is, every ''y'' in ''Y'' is mapped from an element ''x'' in ''X'', more than one ''x'' can map to the same ''y''. '''Left:''' Only one domain is shown which makes ''f'' surjective. '''Right:''' two possible domains ''X''<sub>1</sub> and ''X''<sub>2</sub> are shown.
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