I find this more meaningful when I think of the numbers as arbitrary unordered labels rather than familiar natural numbers. For example, if they were words like

I find this more meaningful when I think of the numbers as arbitrary unordered labels rather than familiar natural numbers. For example, if they were words like “cat” “tree” “nut” etc then the exercise feels more like it's constructing something new, rather than trying to retrofit an axiomatic definition onto a pre-existing structure.