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Revision as of 20:30, 16 November 2012
, 20:30, 16 November 2012→6.31. Relations in General: markup
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If R is tubular at S, then R is called a "partial function" or "prefunction" from S to T, often indicated by writing R = p : S ~> T.
−R = p : S ~> T iff R is tubular at S.+
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−<pre>
+If <math>L\!</math> is tubular at <math>X,\!</math> then <math>L\!</math> is called a ''partial function'' or a ''prefunction'' from <math>X\!</math> to <math>Y,\!</math> indicated by writing <math>L : X \rightharpoonup Y.\!</math> We have the following definitions and notations.
−{| align="center" cellspacing="8" width="90%"
+|
+<math>\begin{array}{lll}
+L ~\text{is a prefunction}~ L : X \rightharpoonup Y
+& \iff &
+L ~\text{is tubular at}~ X.
+\\[6pt]
+L ~\text{is a prefunction}~ L : X \leftharpoonup Y
+& \iff &
+L ~\text{is tubular at}~ Y.
+\end{array}</math>
+|}
+<pre>
If R is a prefunction p : S ~> T that happens to be total at S, then R is called a "function" from S to T, indicated by writing R = f : S > T.
If R is a prefunction p : S ~> T that happens to be total at S, then R is called a "function" from S to T, indicated by writing R = f : S > T.
