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Re: Infinity

• From: ht@markup.co.uk (Henry S. Thompson)
• To: Michael Kay <mike@saxonica.com>
• Date: Sun, 04 Mar 2018 19:37:16 -0500

Michael Kay <mike@saxonica.com> writes:

> ...

> So the value space is infinite, but the lexical space is finite. Or
> is it? Perhaps the set of finite-length strings is itself infinite? 
> <>
>
>  <>
> Does every integer in this infinite set have a finite-length lexical representation? Or are there integers in the value space that have no representation in the lexical space? <>
>
> Whenever I read this, I think, why is that adjective
> "finite-length" there? Would I have to change my software if it were
> removed?

It might have helped (i.e. retained the effect already adverted to by
others of ruling out an infinite stream but made things a bit clearer)
if it had said "finite but unbounded".  Some discussions reserve
'infinite' for cardinalities and prefer 'unbounded' when talking about
lengths or other measures.

That is, just because it's finite doesn't mean there's any upper bound
to what you have to implement in order to correctly claim full
compliance...

Another example that might help: careful mathematical linguists make
different arguments to establish that there is no bound on the length
of an English sentence, from those directed and establishing the
cardinality of the number of English sentences.  See Langendoen,
D. T. and P. M. Postal 1985 _The Vastness of Natural Languages_.

ht
-- 
		    Henry S. Thompson, Markup Systems Ltd.
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• References:
  • Infinity
    • From: Michael Kay <mike@saxonica.com>