Well the identity of % is +inf (also right side only).
I read $n % any( $n..Inf ) == $n. The point is there's no unique right identity and thus (Num,%) disqualifies for a Monoid. BTW, the above is a nice example where a junction needn't be preserved :)
E.g. if X<Y is left associative and returns Y when true then ...
Sorry, is it the case that $x = $y < $z might put something else but 0 or 1 into $x depending on the order relation between $y and $z? -- TSa (Thomas Sandlaß)
