Talk:Relation Isomorphism Preserves Transitivity

I'm not sure that $a \mathcal R b \mathcal R c$ would cause confusion with $\mathcal R$ being ternary.

At least on this site, the notation $a \circ b$, whatever $\circ$ may be (operation or relation) is defined only when $\circ$ is binary. If a relation is ternary, then we use the notation $(a, b, c) \in \circ$ (for a relation) or $\circ (a, b, c)$ for an operation.

I have to confess I've never seen $a \mathcal R b \mathcal R c$ intended to be interpreted as "the ternary relation $\mathcal R$ between $a, b, c$". I rather like the compact nature of $a \mathcal R b \mathcal R c$, as it is even better than $\{(a, b), (b, c)\} \subseteq \mathcal R$ at replacing the unpleasantly unwieldy $a \mathcal R b \land b \mathcal R c$ (or its textual equivalent). --prime mover 18:07, 6 April 2012 (EDT)

I separated it because it confused me for a moment. For common things like $=$ or $\le$ its fine, but for an abstract relation (thinking of $\sim$) its a bit ... uncanny is the word I think. Not to mention when $a \mathcal R b$ might be interpreted as a truth value, and $\mathcal R$ happens to operate on truth values as well; problems with associativity come into play. --Lord_Farin 18:11, 6 April 2012 (EDT)

O yes, hadn't thought of that. Good point. --prime mover 18:12, 6 April 2012 (EDT)