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Infinitesimals exist precisely to create an reciprocal quantity to infinities. Infinitely many finitely short time intervals cannot have passed after finite ti
by notafraudster 4y ago
Infinitesimals exist precisely to create an reciprocal quantity to infinities.
Infinitely many finitely short time intervals cannot have passed after finite time, but infinitely many infinitesimally short time intervals can. In the same way that one way of conceiving infinity is to imagine it as an arbitrarily large value at any given expansion, but infinity in the limit, an infinitesimal is an arbitrarily small value at any given expansion, and zero in the limit.
That's the whole point. The atomic distance of a subdivided step goes to infinitesimal at the same rate that the time associated with the distance does, so we're fine!
- hackandthink 4y agoInfinitesimals 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 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."