I once helped someone set up and tear down a room partition who stressed that the metal poles were numbered and needed to be placed in order. I nodded and followed his direction but something didn’t sit well with me.
He had placed additional structure that wasn’t needed. There wasn’t anything that necessitated an order to what were otherwise indistinguishable poles. In fact, if the property of order was dropped, the task could have been done more quickly without the overhead of keeping track of which pole needed to come before or after another.
It would have been nice if we could have “forgotten” the additional structure of well order-ness to benefit from the more flexible underlying structure. Afterwards, we could have relabeled the newly setup poles. The new ordering would have been indistinguishable from the original proving the additional structure superfluous.