Calculus

[Ouroboros]

@ezzelino

I would disagree with Ouroboros when he states that Aristotle, by positing that the infinitely large and small are beyond the graps of men, blocked the advancement of calculus. In fact, it was quite the opposite. As far as I can tell Aristotle, echoing the prevailing views of mathematicians of his day, was saying that the infinitely large and small are tricky to handle directly (and instead best handled as infinite sets of progressively larger/smaller but finite approximations -- which is exactly the modern approach).

Er, sorry, but he didn’t say that.

It’s confusing because he had two infinities (actually 4, but for this we only talk about those he named “by division”, these which lead to 0 by dividing segments. He was ok with the potential one, which means that it would be ok to go as small as you want, but never get to 0 as you couldn’t complete the process, but not with the actual “infinite division” leading to 0.

Part of his problem of course was that he didn’t had the number 0 as a concept, which is what we use to take the limit and consider his two infinities by division the same.

Shame on me for not remembering before that his problem was lacking a 0 to get to.