A function which is not defined for all arguments of its input type. E.g. f(x) = 1/x if x /= 0. The opposite of a ref="module.php?name=Lexikon&file=search&eid=1&query=total function">total function. In {denotational semantics}, a partial function f : D -> C may be represented as a total function ft : D' -> lift(C) where D' is a superset of D and ft x = f x if x in D ft x = bottom otherwise where lift(C) = C U ref="module.php?name=Lexikon&file=search&eid=1&query=bottom">bottom. Bottom (ref="module.php?name=Lexikon&file=search&eid=1&query=LaTeX">LaTeX ref="module.php?name=Lexikon&file=search&eid=1&query=perp">perp) denotes "undefined". (1995-02-03)

In addition suitable contents:
[ ref="module.php?name=Lexikon&op=content&tid=31">2 ] [ ref="module.php?name=Lexikon&op=content&tid=134">= ] [ ref="module.php?name=Lexikon&op=content&tid=433">al ] [ ref="module.php?name=Lexikon&op=content&tid=544">am ] [ ref="module.php?name=Lexikon&op=content&tid=592">an ] [ ref="module.php?name=Lexikon&op=content&tid=740">ar ] [ ref="module.php?name=Lexikon&op=content&tid=743">arc ] [ ref="module.php?name=Lexikon&op=content&tid=759">arg ] [ ref="module.php?name=Lexikon&op=content&tid=760">argument ] [ ref="module.php?name=Lexikon&op=content&tid=800">as ] [ ref="module.php?name=Lexikon&op=content&tid=894">at ] [ ref="module.php?name=Lexikon&op=content&tid=1025">B ] [ ref="module.php?name=Lexikon&op=content&tid=1026">b ] [ ref="module.php?name=Lexikon&op=content&tid=1181">be ] [ ref="module.php?name=Lexikon&op=content&tid=1444">bo ] [ ref="module.php?name=Lexikon&op=content&tid=1501">bot ] [ ref="module.php?name=Lexikon&op=content&tid=1503">bottom ] [ ref="module.php?name=Lexikon&op=content&tid=1708">C ] [ ref="module.php?name=Lexikon&op=content&tid=2001">ch ] [ ref="module.php?name=Lexikon&op=content&tid=2976">D ] [ ref="module.php?name=Lexikon&op=content&tid=3151">de ] [ ref="module.php?name=Lexikon&op=content&tid=3282">denotational semantics ] [ ref="module.php?name=Lexikon&op=content&tid=3752">du ] [ ref="module.php?name=Lexikon&op=content&tid=3834">E ] [ ref="module.php?name=Lexikon&op=content&tid=3896">ed ] [ ref="module.php?name=Lexikon&op=content&tid=4148">er ] [ ref="module.php?name=Lexikon&op=content&tid=4171">es ] [ ref="module.php?name=Lexikon&op=content&tid=4199">et ] [ ref="module.php?name=Lexikon&op=content&tid=4497">fi ] [ ref="module.php?name=Lexikon&op=content&tid=4520">file ] [ ref="module.php?name=Lexikon&op=content&tid=4700">fo ] [ ref="module.php?name=Lexikon&op=content&tid=4727">for ] [ ref="module.php?name=Lexikon&op=content&tid=4940">function ] [ ref="module.php?name=Lexikon&op=content&tid=5403">gu ] [ ref="module.php?name=Lexikon&op=content&tid=5434">h ] [ ref="module.php?name=Lexikon&op=content&tid=5768">hr ] [ ref="module.php?name=Lexikon&op=content&tid=5931">id ] [ ref="module.php?name=Lexikon&op=content&tid=6013">il ] [ ref="module.php?name=Lexikon&op=content&tid=6064">in ] [ ref="module.php?name=Lexikon&op=content&tid=6165">input ] [ ref="module.php?name=Lexikon&op=content&tid=6413">io ] [ ref="module.php?name=Lexikon&op=content&tid=6482">is ] [ ref="module.php?name=Lexikon&op=content&tid=6558">it ] [ ref="module.php?name=Lexikon&op=content&tid=6989">LaTeX ] [ ref="module.php?name=Lexikon&op=content&tid=7091">Lex ] [ ref="module.php?name=Lexikon&op=content&tid=7107">li ] [ ref="module.php?name=Lexikon&op=content&tid=7463">ma ] [ ref="module.php?name=Lexikon&op=content&tid=7582">man ] [ ref="module.php?name=Lexikon&op=content&tid=8032">mo ] [ ref="module.php?name=Lexikon&op=content&tid=8040">mod ] [ ref="module.php?name=Lexikon&op=content&tid=8079">module ] [ ref="module.php?name=Lexikon&op=content&tid=8386">na ] [ ref="module.php?name=Lexikon&op=content&tid=8460">nc ] [ ref="module.php?name=Lexikon&op=content&tid=8472">ne ] [ ref="module.php?name=Lexikon&op=content&tid=8675">no ] [ ref="module.php?name=Lexikon&op=content&tid=8745">np ] [ ref="module.php?name=Lexikon&op=content&tid=8964">om ] [ ref="module.php?name=Lexikon&op=content&tid=9014">op ] [ ref="module.php?name=Lexikon&op=content&tid=9204">pa ] [ ref="module.php?name=Lexikon&op=content&tid=9457">pe ] [ ref="module.php?name=Lexikon&op=content&tid=9511">perp ] [ ref="module.php?name=Lexikon&op=content&tid=9550">ph ] [ ref="module.php?name=Lexikon&op=content&tid=9908">pr ] [ ref="module.php?name=Lexikon&op=content&tid=10253">query ] [ ref="module.php?name=Lexikon&op=content&tid=10364">rc ] [ ref="module.php?name=Lexikon&op=content&tid=10385">re ] [ ref="module.php?name=Lexikon&op=content&tid=10914">rw ] [ ref="module.php?name=Lexikon&op=content&tid=11150">se ] [ ref="module.php?name=Lexikon&op=content&tid=11215">semantics ] [ ref="module.php?name=Lexikon&op=content&tid=11281">set ] [ ref="module.php?name=Lexikon&op=content&tid=11376">si ] [ ref="module.php?name=Lexikon&op=content&tid=11506">sit ] [ ref="module.php?name=Lexikon&op=content&tid=12133">su ] [ ref="module.php?name=Lexikon&op=content&tid=12359">T ] [ ref="module.php?name=Lexikon&op=content&tid=12360"> ] [ ref="module.php?name=Lexikon&op=content&tid=12588">th ] [ ref="module.php?name=Lexikon&op=content&tid=12721">to ] [ ref="module.php?name=Lexikon&op=content&tid=12761">total function ] [ ref="module.php?name=Lexikon&op=content&tid=12896">tt ] [ ref="module.php?name=Lexikon&op=content&tid=12970">type ] [ ref="module.php?name=Lexikon&op=content&tid=13030">um ] [ ref="module.php?name=Lexikon&op=content&tid=13146">up ] [ ref="module.php?name=Lexikon&op=content&tid=13891">X ]