3 ms·
Here is the thing. Robinson's construction required the axiom of choice and proved that every result that you can prove with infinitesmals has a proof with lim
by btilly 5y ago
Here is the thing.
Robinson's construction required the axiom of choice and proved that every result that you can prove with infinitesmals has a proof with limits without the axiom of choice. But he went on to show that infinitesmals allowed abandoned proofs to be made rigorous, and claimed that they were good for intuition.
In other words infinitesmals were trying to replace something that had become established. The axioms behind the established thing are much weaker than the axioms required for infinitesmals. And infinitesmals provably don't let you prove anything fundamentally new.
At that point any interest in infinitesmals has to come down to curiosity and the claim that it helps intuition. As for curiosity, I'm glad to have understood them. As for helping intuition, that is in the eye of the beholder, and has not been a compelling enough argument to get people to switch.