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Revision as of 17:54, 27 November 2007
, 17:54, 27 November 2007→Commentary Note 11.8: markup
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Clearly, if any relation is (≤''c'')-regular on one of its domains ''X''<sub>''j''</sub> and also (≥''c'')-regular on the same domain, then it must be (=''c'')-regular on the affected domain ''X''<sub>''j''</sub>, in effect, ''c''-regular at ''j''.
Clearly, if any relation is (=<c)-regular on one
of its domains X_j and also (>=c)-regular on the
same domain, then it must be (=c)-regular on the
affected domain X_j, in effect, c-regular at j.
For example, let G = {r, s, t} and H = {1, ..., 9},
For example, let ''G'' = {''r'', ''s'', ''t'} and ''H'' = {1, …, 9}, and consider the 2-adic relation ''F'' ⊆ ''G'' × ''H'' that is bigraphed here:
and consider the 2-adic relation F c G x H that is
bigraphed here:
<pre>
r s t
r s t
o o o G
o o o G
o o o o o o o o o H
o o o o o o o o o H
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
</pre>
We observe that F is 3-regular at G and 1-regular at H.
We observe that ''F'' is 3-regular at ''G'' and 1-regular at ''H''.
===Commentary Note 11.9===
===Commentary Note 11.9===
