function
1. ematics> (Or "map", "mapping") If D and C are sets (the domain and codomain) then a function f from D to C, normally written "f : D -> C" is a subset of D x C such that: 1. For each d in D there exists some c in C such that (d,c) is an element of f. I.e. the function is defined for every element of D. 2. For each d in D, c1 and c2 in C, if both (d,c1) and (d,c2) are elements of f then c1 = c2. I.e. the function is uniquely defined for every element of D. See also ef="module.php?name=Lexikon&file=search&eid=1&query=image">image, ef="module.php?name=Lexikon&file=search&eid=1&query=inverse">inverse, ef="module.php?name=Lexikon&file=search&eid=1&query=partial function">partial function. 2. Computing usage derives from the mathematical term but is much less strict. In programming (except in ef="module.php?name=Lexikon&file=search&eid=1&query=functional programming">functional programming), a function may return different values each time it is called with the same argument values and may have ef="module.php?name=Lexikon&file=search&eid=1&query=side effects">side effects. A ef="module.php?name=Lexikon&file=search&eid=1&query=procedure">procedure is a function which returns no value but has only ef="module.php?name=Lexikon&file=search&eid=1&query=side-effects">side-effects. The ef="module.php?name=Lexikon&file=search&eid=1&query=C">C language, for example, has no procedures, only functions. ef="module.php?name=Lexikon&file=search&eid=1&query=ANSI C">ANSI C even defines a ef="module.php?name=Lexikon&file=search&eid=1&query=type">type, ef="module.php?name=Lexikon&file=search&eid=1&query=void">void, for the result of a function that has no result. (1996-09-01) e="border-width:thin; border-color:#333333; border-style:dashed; padding:5px;" align="left">In addition suitable contents:
[ ef="module.php?name=Lexikon&op=content&tid=31">2 ] [ ef="module.php?name=Lexikon&op=content&tid=134">= ] [ ef="module.php?name=Lexikon&op=content&tid=396">ag ] [ ef="module.php?name=Lexikon&op=content&tid=411">ai ] [ ef="module.php?name=Lexikon&op=content&tid=433">al ] [ ef="module.php?name=Lexikon&op=content&tid=544">am ] [ ef="module.php?name=Lexikon&op=content&tid=592">an ] [ ef="module.php?name=Lexikon&op=content&tid=639">ANS ] [ ef="module.php?name=Lexikon&op=content&tid=641">ANSI ] [ ef="module.php?name=Lexikon&op=content&tid=642">ANSI C ] [ ef="module.php?name=Lexikon&op=content&tid=683">app ] [ ef="module.php?name=Lexikon&op=content&tid=740">ar ] [ ef="module.php?name=Lexikon&op=content&tid=743">arc ] [ ef="module.php?name=Lexikon&op=content&tid=759">arg ] [ ef="module.php?name=Lexikon&op=content&tid=760">argument ] [ ef="module.php?name=Lexikon&op=content&tid=800">as ] [ ef="module.php?name=Lexikon&op=content&tid=894">at ] [ ef="module.php?name=Lexikon&op=content&tid=996">av ] [ ef="module.php?name=Lexikon&op=content&tid=1026">b ] [ ef="module.php?name=Lexikon&op=content&tid=1444">bo ] [ ef="module.php?name=Lexikon&op=content&tid=1501">bot ] [ ef="module.php?name=Lexikon&op=content&tid=1606">bs ] [ ef="module.php?name=Lexikon&op=content&tid=1708">C ] [ ef="module.php?name=Lexikon&op=content&tid=1724">ca ] [ ef="module.php?name=Lexikon&op=content&tid=2001">ch ] [ ef="module.php?name=Lexikon&op=content&tid=2247">co ] [ ef="module.php?name=Lexikon&op=content&tid=2293">codomain ] [ ef="module.php?name=Lexikon&op=content&tid=2976">D ] [ ef="module.php?name=Lexikon&op=content&tid=3151">de ] [ ef="module.php?name=Lexikon&op=content&tid=3371">diff ] [ ef="module.php?name=Lexikon&op=content&tid=3565">do ] [ ef="module.php?name=Lexikon&op=content&tid=3595">domain ] [ ef="module.php?name=Lexikon&op=content&tid=3752">du ] [ ef="module.php?name=Lexikon&op=content&tid=3865">ec ] [ ef="module.php?name=Lexikon&op=content&tid=3896">ed ] [ ef="module.php?name=Lexikon&op=content&tid=3923">edu ] [ ef="module.php?name=Lexikon&op=content&tid=3929">ee ] [ ef="module.php?name=Lexikon&op=content&tid=4008">element ] [ ef="module.php?name=Lexikon&op=content&tid=4148">er ] [ ef="module.php?name=Lexikon&op=content&tid=4171">es ] [ ef="module.php?name=Lexikon&op=content&tid=4199">et ] [ ef="module.php?name=Lexikon&op=content&tid=4497">fi ] [ ef="module.php?name=Lexikon&op=content&tid=4520">file ] [ ef="module.php?name=Lexikon&op=content&tid=4700">fo ] [ ef="module.php?name=Lexikon&op=content&tid=4727">for ] [ ef="module.php?name=Lexikon&op=content&tid=4828">fr ] [ ef="module.php?name=Lexikon&op=content&tid=4941">functional ] [ ef="module.php?name=Lexikon&op=content&tid=4946">functional program ] [ ef="module.php?name=Lexikon&op=content&tid=4947">functional programming ] [ ef="module.php?name=Lexikon&op=content&tid=5057">ge ] [ ef="module.php?name=Lexikon&op=content&tid=5291">gr ] [ ef="module.php?name=Lexikon&op=content&tid=5403">gu ] [ ef="module.php?name=Lexikon&op=content&tid=5434">h ] [ ef="module.php?name=Lexikon&op=content&tid=5540">hat ] [ ef="module.php?name=Lexikon&op=content&tid=5768">hr ] [ ef="module.php?name=Lexikon&op=content&tid=5931">id ] [ ef="module.php?name=Lexikon&op=content&tid=5986">iff ] [ ef="module.php?name=Lexikon&op=content&tid=6013">il ] [ ef="module.php?name=Lexikon&op=content&tid=6024">image ] [ ef="module.php?name=Lexikon&op=content&tid=6064">in ] [ ef="module.php?name=Lexikon&op=content&tid=6407">inverse ] [ ef="module.php?name=Lexikon&op=content&tid=6413">io ] [ ef="module.php?name=Lexikon&op=content&tid=6446">iq ] [ ef="module.php?name=Lexikon&op=content&tid=6482">is ] [ ef="module.php?name=Lexikon&op=content&tid=6558">it ] [ ef="module.php?name=Lexikon&op=content&tid=6918">la ] [ ef="module.php?name=Lexikon&op=content&tid=6950">language ] [ ef="module.php?name=Lexikon&op=content&tid=7091">Lex ] [ ef="module.php?name=Lexikon&op=content&tid=7399">ls ] [ ef="module.php?name=Lexikon&op=content&tid=7410">lt ] [ ef="module.php?name=Lexikon&op=content&tid=7415">lu ] [ ef="module.php?name=Lexikon&op=content&tid=7441">ly ] [ ef="module.php?name=Lexikon&op=content&tid=7463">ma ] [ ef="module.php?name=Lexikon&op=content&tid=7579">mall ] [ ef="module.php?name=Lexikon&op=content&tid=7607">map ] [ ef="module.php?name=Lexikon&op=content&tid=7610">mapping ] [ ef="module.php?name=Lexikon&op=content&tid=8019">mm ] [ ef="module.php?name=Lexikon&op=content&tid=8032">mo ] [ ef="module.php?name=Lexikon&op=content&tid=8040">mod ] [ ef="module.php?name=Lexikon&op=content&tid=8079">module ] [ ef="module.php?name=Lexikon&op=content&tid=8167">mp ] [ ef="module.php?name=Lexikon&op=content&tid=8258">mu ] [ ef="module.php?name=Lexikon&op=content&tid=8384">N ] [ ef="module.php?name=Lexikon&op=content&tid=8386">na ] [ ef="module.php?name=Lexikon&op=content&tid=8460">nc ] [ ef="module.php?name=Lexikon&op=content&tid=8472">ne ] [ ef="module.php?name=Lexikon&op=content&tid=8627">ng ] [ ef="module.php?name=Lexikon&op=content&tid=8630">ni ] [ ef="module.php?name=Lexikon&op=content&tid=8660">nl ] [ ef="module.php?name=Lexikon&op=content&tid=8675">no ] [ ef="module.php?name=Lexikon&op=content&tid=8718">norm ] [ ef="module.php?name=Lexikon&op=content&tid=8760">ns ] [ ef="module.php?name=Lexikon&op=content&tid=8770">NSI ] [ ef="module.php?name=Lexikon&op=content&tid=8820">O ] [ ef="module.php?name=Lexikon&op=content&tid=8964">om ] [ ef="module.php?name=Lexikon&op=content&tid=9204">pa ] [ ef="module.php?name=Lexikon&op=content&tid=9332">partial function ] [ ef="module.php?name=Lexikon&op=content&tid=9457">pe ] [ ef="module.php?name=Lexikon&op=content&tid=9550">ph ] [ ef="module.php?name=Lexikon&op=content&tid=9616">ping ] [ ef="module.php?name=Lexikon&op=content&tid=9651">pl ] [ ef="module.php?name=Lexikon&op=content&tid=9908">pr ] [ ef="module.php?name=Lexikon&op=content&tid=9994">procedure ] [ ef="module.php?name=Lexikon&op=content&tid=10023">program ] [ ef="module.php?name=Lexikon&op=content&tid=10042">programming ] [ ef="module.php?name=Lexikon&op=content&tid=10144">pt ] [ ef="module.php?name=Lexikon&op=content&tid=10253">query ] [ ef="module.php?name=Lexikon&op=content&tid=10364">rc ] [ ef="module.php?name=Lexikon&op=content&tid=10385">re ] [ ef="module.php?name=Lexikon&op=content&tid=10767">ro ] [ ef="module.php?name=Lexikon&op=content&tid=10918">S ] [ ef="module.php?name=Lexikon&op=content&tid=10922">sa ] [ ef="module.php?name=Lexikon&op=content&tid=10959">sam ] [ ef="module.php?name=Lexikon&op=content&tid=11150">se ] [ ef="module.php?name=Lexikon&op=content&tid=11281">set ] [ ef="module.php?name=Lexikon&op=content&tid=11375">SI ] [ ef="module.php?name=Lexikon&op=content&tid=11376">si ] [ ef="module.php?name=Lexikon&op=content&tid=11382">side-effect ] [ ef="module.php?name=Lexikon&op=content&tid=11651">so ] [ ef="module.php?name=Lexikon&op=content&tid=11934">st ] [ ef="module.php?name=Lexikon&op=content&tid=12090">strict ] [ ef="module.php?name=Lexikon&op=content&tid=12133">su ] [ ef="module.php?name=Lexikon&op=content&tid=12359">T ] [ ef="module.php?name=Lexikon&op=content&tid=12588">th ] [ ef="module.php?name=Lexikon&op=content&tid=12721">to ] [ ef="module.php?name=Lexikon&op=content&tid=12787">tr ] [ ef="module.php?name=Lexikon&op=content&tid=12896">tt ] [ ef="module.php?name=Lexikon&op=content&tid=12970">type ] [ ef="module.php?name=Lexikon&op=content&tid=12986">ua ] [ ef="module.php?name=Lexikon&op=content&tid=13030">um ] [ ef="module.php?name=Lexikon&op=content&tid=13175">us ] [ ef="module.php?name=Lexikon&op=content&tid=13252">va ] [ ef="module.php?name=Lexikon&op=content&tid=13260">value ] [ ef="module.php?name=Lexikon&op=content&tid=13310">ve ]
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