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> that allow us to do arithmetic with arbitrary real numbers Of course there are. You can symbolically encode and manipulate real numbers with exact precision.
by WastingMyTime89 5y ago
> that allow us to do arithmetic with arbitrary real numbers
Of course there are. You can symbolically encode and manipulate real numbers with exact precision. Sure it might become unwieldy and is fundamentaly constrained by the physical limits of your computer but the same is true with large integers computation.
People don't do it usually because it's useless not because it's impossible. Bounded precision is fine most of the time.
- anchpop 5y agoThat doesn’t let you work with arbitrary real numbers because the vast majority of real numbers cannot by symbolicly encoded, even on a turing machine with infinite memory
- Firadeoclus 5y agoIf they cannot be symbolically encoded why would you ever _need_ to encode them?
- anchpop 5y agoNot being able to do something has never stopped people from needing to do it :P That said, with Google's paper "towards an api for the real numbers", you get close enough for many practical purposes