What math is useful for distinguishing and classifying things based only on relations they satisfy?(adsbygoogle = window.adsbygoogle || []).push({});

For example the relation ##R_1 = \{(a,b), (b,a)\}## isn't useful for distinguishing "a" from "b" while the relation ##R_2 = \{(a,b), (c,b) \}## lets us distinguish "b" by the description "The thing that has two other things ##R_2## related to it".

In a more general case, we could have sets of symbols that satisfy more than one relation - or even infinite sets of symbols.

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# I Distinguishing things by relations

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