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Infinitesimals are just a different aspect of mathematical infinity. This is the magic that makes calculus work (from a formal standpoint).
by jyounker 5y ago
Infinitesimals are just a different aspect of mathematical infinity.
This is the magic that makes calculus work (from a formal standpoint).
- im3w1l 5y agoWhile you can build a calculus using infinitesimals, the usual construction does not use them. https://en.wikipedia.org/wiki/Nonstandard_analysis https://en.wikipedia.org/wiki/Nonstandard_analysis
- anikan_vader 5y agoThe original construction did though, if you look at the writings of Newton/Leibniz. But their work was totally hand-wavey. Cauchy discovered limits in the 1800s, and it wasn’t until the 20th century that the original idea of infinitesimals was formalized. In some sense we have come full circle. I do think that infinitesimals are a much more intuitive way to understand calculus. It’s a shame it took so long to find positive numbers less than any real.