There are advantages and disadvantages both ways. If the name “order” comes last, then the order axioms will appear unmotivated and arbitrary to the student. I’m not sure what the best thing to do is.
We want something that corresponds to the intuitive idea of order. Let’s unpack this intuition. Now, given that some relation R has those properties we are then justified in using the symbol ≤.
In other words, you don’t need to hide your destination—you just need to make it clear that intuitive labels are a privilege entitled to objects that have demonstrated good behavior.
There are advantages and disadvantages both ways. If the name “order” comes last, then the order axioms will appear unmotivated and arbitrary to the student. I’m not sure what the best thing to do is.
I’d recommend something like
In other words, you don’t need to hide your destination—you just need to make it clear that intuitive labels are a privilege entitled to objects that have demonstrated good behavior.