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I think this is the wrong question. Any number, if you define them as a representation of digits, is computable in that sense. What isn't necessary computable i

I think this is the wrong question. Any number, if you define them as a representation of digits, is computable in that sense. What isn't necessary computable is the value of a function taken with a certain input or input range. BB numbers, as large as they can be, are themselves finite and therefore "computable" once you know them, but the mapping from natural numbers to BB numbers is not computable. So the real value of a particular function f evaluated at some number say 100 could be as small as 0, but maybe you just can't compute f(100) and know that it's 0.

teraflop 3y ago
> Any number, if you define them as a representation of digits, is computable in that sense. You have to be a bit careful, here. What you're saying is true of integers (such as the values taken by the BB function), as well as rationals. But it's not true of real numbers, because the reals are uncountable, and therefore there are infinitely many real numbers that cannot be finitely "described" or written down (in whatever notation you happen to care about). An example of an uncomputable real number: https://en.wikipedia.org/wiki/Chaitin%27s_constant https://en.wikipedia.org/wiki/Chaitin%27s_constant