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/sci/ - Science & Math

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8093299 No.8093299 [Reply] [Original]

Doesn't lazy evaluation, particularly that found in Haskell, serve as a direct counterexample to Wildberger's objections to the computability of infinite sets?

>> No.8093308

>>8093299
Nope. When Wildberger talks about a computable number, he means one that can be computed as a decimal approximation to an arbitrary number of decimal places. Lazy evaluation, as cool as it is, just means that evaluation can be deferred if you only ever end up accessing a finite portion of an infiinite set.

>> No.8093309

>>8093299
In Wildberger's view, a computation should be well defined and have an end, and that's completely different from Haskell.

>> No.8093312

>>8093308
Then what's the practical difference from a finite set that's too large for us to compute, versus an infinite set which we also can't compute?

>> No.8093313

>>8093309
this is not necessarily what that means. Computable numbers have a well-defined meaning in terms of decimal representations.

>> No.8093320

>>8093312
In this context, computability is a property of the numbers in a set, not the set itself. You can talk about the computable and non-computable real numbers, but its not a property of the whole set.

>> No.8093327

>>8093320
I should mention that computable sets actually are a thing, but that's not the same thing as what's being discussed here. Computability of sets has to do with determining if an object is contained in it or not,