Talk:Proof: Difference between revisions
changed a phrasing, and a reaction to a non-argument
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:: Ok, that's ambiguous terminology. I agree that "countable" in the mathematical sense means aleph null style infinity -- "has a one-to-one correspondence with natural numbers".
:: However, in a computer program, an infinity of values cannot be implemented -- it can be symbolized, but that is different from implementing it. A computer program can only implement a finite set of distinct values. Thus, in the context of a type -- when using the normal meanings of "countable" and "type" -- natural numbers are not countable.
:: That said, if you really mean for a program to implement a "countably infinite" type, that is itself a failure in specification. At the very least, you should be obligated to say what you mean by "type" when the usual meaning of type in programming refers to something which can only enumerate a finite set of values without failure.
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::::: Typically a type, in computer programming, symbolizes a set of values which may validly be represented in the computer program. If the set is infinite, however, the validity requirement vanishes. --[[User:Rdm|Rdm]] 22:27, 13 May 2012 (UTC)
:::::: Not even wrong... I don't think it will be fruitful to continue this discussion. —''[[User:Ruud Koot|Ruud]]'' 22:41, 13 May 2012 (UTC)
::::::: Typically "not even wrong" indicates a lack of testability. It's not clear how that is relevant here. I am guessing, though, that you disagree with me about the meaning of the word type. But if that were the case I think you should present your own definition.
::::::: My suspicion though, is that in this case "not even wrong" means the same thing as "right". --[[User:Rdm|Rdm]] 00:21, 14 May 2012 (UTC)
::: > However, in a computer program, an infinity cannot be implemented
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