Infinitesimals are cool but I think this is not really about infinitesimals - it is about ordinary real numbers.

(so I think this is not true: "Infinitely many finitely short time intervals cannot have passed after finite time")

(I agree here: "infinitely many infinitesimally" is finite) (an infinitesimal is smaller than any real number, especially smaller than 1/n for every natural number)

https://en.wikipedia.org/wiki/Infinitesimal

"Infinitesimals were the subject of political and religious controversies in 17th century Europe, including a ban on infinitesimals issued by clerics in Rome in 1632."