Predicates variable order in P(x,y)

Question

Is the predicate P with two variables, x and y, x smaller than y , the same thing as the predicate P with two variable , y and x, does it stays x smaller than y or does y becomes smaller than x ?

Thanks.

Answer 1

If the predicate $P(x,y)$ is defined to mean $x<y$, then $P(y,x)$ means $y<x$. The names of the variables don’t matter, but their position among the arguments of $P$ does, so it’s always $$\text{first argument}<\text{second argument}\;.$$