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Different strokes for different folks and all that but the concept of infinity doesn't really bother me that much because it doesn't really exist to me as a num
by noobermin 4y ago
Different strokes for different folks and all that but the concept of infinity doesn't really bother me that much because it doesn't really exist to me as a number more than it is a fact of the unbounded-ness of some set with a total ordering. It is more a statement of potential rather than actual existence, that given an infinite set, you can always find a "larger" element, which to me is just a result of the way it is defined.
Infinitesimals to me are a bit more difficult because physics (the real world) doesn't actually need real continuity, otherwise physical models won't work because many continuous quantities in physics (fluid densities, temperatures, etc) aren't really continuous on small scales compared to the problem size, but that isn't needed to model such systems well. It seems like there are only a few pathological examples mathematicians come up with which is interesting and fascinating that require actual continuity, but most physical systems do not need real, actual continuity.
On the same token, I guess (countable) infinite sets aren't really needed either.
- ravi-delia 4y agoI think that's why it's so handy to start with epsilon delta limits, or even better sequence limits. Once you can screen off "infinitely" to "arbitrarily" and see when and where the substitution works, you're golden. Of course there are other things in math which might rightfully be called "infinity" but they don't come up in high school calculus