Additive function: Difference between revisions

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{{more footnotes|date=February 2013}} 200000132648

In [[mathematics]] the term '''additive function''' has two different definitions, depending on the specific field of application.

In [[algebra]] an '''{{anchor|definition-additive_additive_function-algebra}}additive function''' (or '''additive map''') is a function that preserves the addition operation:

function-algebra}}additive function''' (or '''additive map''') is a function that preserves the addition operation:

:''f''(''x'' + ''y'') = ''f''(''x'') + ''f''(''y'')

for any two elements ''x'' and ''y'' in the ___domain. For example, any [[linear map]] is additive. When the ___domain is the [[real numbers]], this is [[Cauchy's functional equation]].