Talk:Strictly Increasing Mapping is Increasing

I don't know, could it just be substitution? if $x=y$ then we can simply substitute y for one of the x's in $\phi(x)=\phi(x)$ which is true by the reflexivity of =. I don't know if you've established substitution and reflexivity of = yet, though.--cynic 16:39, 27 August 2008 (UTC)

Duh! Silly me. Of course it follows. After all, it's a mapping, and that's what a mapping does: $x = y \rightarrow f(x) = f(y)$. --Matt Westwood 19:34, 27 August 2008 (UTC)

And of course "equals" is "equals" - none of that namby-pamby rubbish about how equals on one ordering may be a different sort of equals from that on the other ordering, no matter that the actual orderings themselves may be different (hence the $\le_1, \le_2$. So $=_1$ and $=_2$ is plain stoopid.