Talk:Proof: Difference between revisions

Content added Content deleted
(changed a phrasing, and a reaction to a non-argument)
Line 217: Line 217:


::: Yes, linked lists is a countably infinite data type, this means that there is a countably many linked lists that can be (potentially) constructed. In contrast, the boolean data type has the cardinality = 2.
::: Yes, linked lists is a countably infinite data type, this means that there is a countably many linked lists that can be (potentially) constructed. In contrast, the boolean data type has the cardinality = 2.

:::: This is trivially false, since every computer has a finite amount of memory -- even if it's virtual memory -- and linked lists must fit in memory or the links are invalid. At most, the number of linked lists which can be represented is the factorial of 2^N where N is the number of bits of memory (N is wordsize * 2^64 in a computer with 64 bit addressing). Now, I will agree that that is a large number, which might distract you from noticing that it's a finite number, but it's still finite. And even if you changed from a parallel bit implementation to a serial bit implementation and addresses were represented by a sequence of 1 bits (the first 0 terminating them), which would let you have arbitrarily long addresses, you still run into issues like the lifetime of the universe (or, more practically, the funding which keeps your computer system running). It's still not infinite, except in your imagination. --[[User:Rdm|Rdm]] 01:44, 14 May 2012 (UTC)


::: See also this link: http://okmij.org/ftp/Computation/uncountable-sets.html.
::: See also this link: http://okmij.org/ftp/Computation/uncountable-sets.html.