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Revision as of 16:08, 16 November 2012
, 16:08, 16 November 2012→Relations
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==Relations==
==Relations In General==
Next let's re-examine the ''numerical incidence properties'' of relations, concentrating on the definitions of the assorted regularity conditions.
Next let's re-examine the ''numerical incidence properties'' of relations, concentrating on the definitions of the assorted regularity conditions.
& \iff &
& \iff &
P ~\text{is}~ 1\text{-regular at}~ Y.
P ~\text{is}~ 1\text{-regular at}~ Y.
\end{array}</math>
|}
In the case of a 2-adic relation <math>F \subseteq X \times Y</math> that has the qualifications of a function <math>f : X \to Y,</math> there are a number of further differentia that arise:
{| align="center" cellspacing="6" width="90%"
|
<math>\begin{array}{lll}
f ~\text{is surjective}
& \iff &
f ~\text{is total at}~ Y.
\\[6pt]
f ~\text{is injective}
& \iff &
f ~\text{is tubular at}~ Y.
\\[6pt]
f ~\text{is bijective}
& \iff &
f ~\text{is}~ 1\text{-regular at}~ y.
\end{array}</math>
\end{array}</math>
|}
|}
