[Patient0]

For me it was completely the other way around: I was "taught" calculus using the infinitesimal approach but without any rigour. Statements like "As dx gets really really small x+dx/x becomes 1" drove me crazy! Why was it sometimes ok to replace dx with 0!? The idea of an "infinitely" small number to me was always vague and suspect. So while I could do the calculations I never trusted the results.

This meant that maths stopped having the same appeal to me as computer programming.

It was only years later when I revisited the epsilon delta arguments that it finally made sense. It was a revelation to me that you could explain all of calculus without ever talking about "infinite".

I wish it had been taught to me rigorously the first time around: I would have been much better off.