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I think the math you've been exposed to is mostly on the computational side (compute an integral, solve an equation, etc). Much (most?) of math is quite differ
by BeetleB 4y ago
I think the math you've been exposed to is mostly on the computational side (compute an integral, solve an equation, etc).
Much (most?) of math is quite different from it. Proving that there is a well ordering of the reals, and simultaneously proving that it is impossible to show you such an ordering: Very different from skills needed in programming.
- edgyquant 4y agoI disagree. You’re only able to prove that ordering of the reals (and that it’s impossible to show) because you are computing the abstract structure underlying the reals (which is based on some lower level ideas etc.) Just because a problem is computationally hard with a step by step CPU doesn’t mean it isn’t computation. This is actually a problem of interest to me, so I’ve definitely been exposed to it and the limits of modern computation. But I’m not speaking strictly about the modern day CPU.
- bmitc 4y ago> You’re only able to prove that ordering of the reals (and that it’s impossible to show) because you are computing the abstract structure underlying the reals (which is based on some lower level ideas etc.) Just because a problem is computationally hard with a step by step CPU doesn’t mean it isn’t computation. The set of computable real numbers is countable and thus has measure zero. In other words, almost all real numbers are non-computable, and almost all has an exact definition. So you can’t compute the real numbers unless you’re meaning something else by computing.