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On Tuesday, June 28, 2016 at 11:42:29 AM UTC+5:30, Gregory Ewing wrote: > Rustom Mody wrote: > > I said that for the Haskell list [0..] > > > > [0..] ++ [-1] == [0..] > > > > He said (in effect) yes that -1 would not be detectable but its still there! > > The code to generate it is there, but it will never > be executed, so the compiler is entitled to optimise > it away. :-) > > He may have a point though. There are avenues of > mathematics where people think about objects such > as "all the natural numbers, followed by -42", and > consider that to be something different from just > "all the natural numbers". > > So, a mathematician would probably say they're not > equal. A scientist would say they may or may not be > equal, but the difference is not testable. > > An engineer would say "Lessee, 0, 1, 2, 3, 4, 5, > 6, 7... yep, they're equal to within measurement > error." Yes there is a sloppiness in my statement above: [0..] ++ [-1] == [0..] What kind of '==' is that? If its the Haskell (or generally, programming language implementation) version that expression just hangs trying to find the end of the infinite lists. If its not then a devil's advocate could well say: "So its metaphysical, theological and can know the unknowable, viz. that that -1 which is computationally undetectable is nevertheless present. ie the '++' can be a lazy Haskell *implemented* function The '==' OTOH is something at least quasi mystical Mathematicians are more likely to say 'mathematical' than 'mystical' Such mathematicians -- the majority -- are usually called 'Platonists'

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