Changes

Clearly, if any relation is <math>(\le c)\text{-regular}</math> on one of its domains <math>X_j\!</math> and also <math>(\ge c)\text{-regular}</math> on the same domain, then it must be <math>(= c)\text{-regular}\!</math> on that domain, in effect, <math>c\text{-regular}\!</math> at <math>j.\!</math>

Clearly, if any relation is <math>(\le c)\text{-regular}</math> on one of its domains <math>X_j\!</math> and also <math>(\ge c)\text{-regular}</math> on the same domain, then it must be <math>(= c)\text{-regular}\!</math> on that domain, in effect, <math>c\text{-regular}\!</math> at <math>j.\!</math>

For example, let ''G'' = {''r'',&nbsp;''s'',&nbsp;''t''} and ''H'' = {1,&nbsp;&hellip;,&nbsp;9}, and consider the 2-adic relation ''F''&nbsp;&sube;&nbsp;''G''&nbsp;&times;&nbsp;''H'' that is bigraphed here:

For example, let <math>G = \{ r, s, t \}\!</math> and <math>H = \{ 1, \ldots, 9 \},\!</math> and consider the 2-adic relation <math>F \subseteq G \times H</math> that is bigraphed here:

<pre>

<pre>

     r          s          t

     r          s          t

1  2  3  4  5  6  7  8  9

1  2  3  4  5  6  7  8  9

</pre>

</pre>

We observe that ''F'' is 3-regular at ''G'' and 1-regular at ''H''.

We observe that <math>F\!</math> is 3-regular at <math>G\!</math> and 1-regular at <math>H.\!</math>

===Commentary Note 11.9===

===Commentary Note 11.9===