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Re: Infinity

• From: "C. M. Sperberg-McQueen" <cmsmcq@blackmesatech.com>
• To: Tim Bray <tbray@textuality.com>
• Date: Mon, 5 Mar 2018 08:27:36 -0700

> On Mar 4, 2018, at 10:36 PM, Tim Bray <tbray@textuality.com> wrote:
> 
> 
> 
> On Sun, Mar 4, 2018 at 6:36 PM, C. M. Sperberg-McQueen <cmsmcq@blackmesatech.com> wrote:
> 
> I would not like to have to write the test cases for checking that
> a conforming processor either accepts a string consisting of an
> infinite number of occurrences of the digit ‘0’ followed by the digit
> ‘5’, or else raises an out-of-resources error, and that the processor
> rejects a string consisting of the letter ‘B’ preceded by an infinite
> number of occurrences of the digit ‘0’.
> 
> ​Actually, a state-machine based implementation can report with high confidence, and with strict bounds on memory usage, the presence, or failure to be present, of a '5' after any number of 0's. Infinity isn't a thing that exists in actual texts, so there's no need to state that any given string must be finite.  

I think you are offering to pass the test. But you haven’t shown how to
write it.  

Nor is your claim that such a test would be unnecessary because the
spec somehow COULD NOT allow infinite-length lexical representations
a plausible one.

If you would like to undertake a proof that “infinity isn’t a thing that exists 
in actual texts” that doesn’t amount to the ex cathedra claim that the
text containing an infinite number of zeroes followed by a five is not an
“actual” text, and without assuming the kind of memory and representation
of strings most commonly used today, I would be interested in seeing the
proof.

> The closest you can get is say “any number of” and there you go.

If all you mean is that instead of saying explicitly that the string is
finite, the spec can say other things which have the same effect, then
I agree.  But specifying that the lexical representation of an integer
may consist of any number of digits will merely cause the underlying
question to take the form “what if the number is infinity?”, and since
not every reader of English has the deep instinct that infinity is not
a number (indeed, in many ways infinity is treated as a number in
algebra and calculus, as the wikipedia article on Aleph_one already
cited in this  

********************************************
C. M. Sperberg-McQueen
Black Mesa Technologies LLC
cmsmcq@blackmesatech.com
http://www.blackmesatech.com
********************************************

• References:
  • Infinity
    • From: Michael Kay <mike@saxonica.com>
  • Re: Infinity
    • From: Elliotte Rusty Harold <elharo@ibiblio.org>
  • Re: Infinity
    • From: C. M. Sperberg-McQueen <cmsmcq@blackmesatech.com>
  • Re: Infinity
    • From: Tim Bray <tbray@textuality.com>