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Anything that deals with calculus has infinities underneath. Much of the modern technology wouldn’t exist if we wouldn’t know calculus. Also, check out Fourier
by kolinko 5y ago
Anything that deals with calculus has infinities underneath. Much of the modern technology wouldn’t exist if we wouldn’t know calculus.
Also, check out Fourier transform and try to rewrite it without infinities - https://bookdown.org/vshahrez/lecture-notes/fourier-transforms.html https://bookdown.org/vshahrez/lecture-notes/fourier-transfor... . Without fourier transform we wouldn’t have mp3, and the whole field of signal processing if I’m not mistaken.
Without signal processing we would not have long distance digital communication.
- TchoBeer 5y agoYou can make calculus and Fourier transforms without infinite sets; all you need is limits.
- jlokier 5y agoIndeed you can. But you can also make calculus without limits, using explicit definitions of infinitesimals (called non-standard analysis or non-standard calculus), and in some ways this is simpler to use. You can approach it either way. As limits, or by extending the number system with particular consistent definitions of infinitesimals and infinities. In practice using infinitesimals is often what people actually do when using calculus anyway, even when mentioning the limit in a sloppy hand-wave in the background, so it's good that non-standard analysis shows that the simpler method people actually use is usually logically coherent and gives the same answers as limits.