Constant function: Difference between revisions

Revision as of 00:54, 10 November 2005

Revision as of 00:54, 10 November 2005

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In [[mathematics]] a '''constant function''' is a [[function (mathematics)|function]] whose values do not vary and thus are [[constant]]. For example, if we have the function ''f''(''x'') = 4 for any ''x'', then ''f'' is constant since f maps any value to 4. More formally, a function ''f'' : ''A'' → ''B'', is a constant function if ''f''(''x'') = ''f''(''y'') for all ''x'' and ''y'' in ''A''.

Notice that every [[empty function]], that is, any function whose [[___domain]] equals the [[empty set]], is included in the above definition [[vacuous truth|vacuously]], since there are no ''x'' and ''y'' in ''A'' for which ''f''(''x'') and ''f''(''y'') are different. However some find it more convenient to define constant function so as to exclude empty functions.