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Re: Matheology sqrt(2): WM admits to unlistability of 0/1 sequences
Posted:
Dec 20, 2013 3:38 PM


On Friday, December 20, 2013 2:54:53 PM UTC4, muec...@rz.fhaugsburg.de wrote: > On Friday, 20 December 2013 18:55:58 UTC+1, wpih...@gmail.com wrote: > > > > > > > > > > > > No. Counterexample: The potentially infinite sequence of 1's is given by many finite formulas like 1/9 or "0.111..." or "the potentially infinite sequence of 1's behind the point", which are not the sequence but determine the sequence: > > > > > > > > > > > > So what. There is nothing in the definition of the potentially infinite > > > > > > list L that says that two elements of L cannot be the same, > > > > Correct. > > > > > > (Note if two formula produce the same value for any n in N > > > > > > they are by definition equal as potentially infinite sequences) > > > > The formulas are different by their letters but identical by their result, just like a and b differ although they may stand for the same number in a = b.
So there is a list of finite formula which produce 0/1 sequences but no list of the potentially infinite 0/1 sequences to which they correspond.
William Hughes



