Re: [xml-dev] Infinity

["Norman Gray" <norman@astro.gla.ac.uk>]

Greetings.

On 3 Mar 2018, at 10:56, Elliotte Rusty Harold wrote:

> Yes, the spec is correct on this point. Every integer has a finite
> length representation. The infinite part refers to the number of
> integers, not the length of each integer's string representation.
In addition, it might be that the distinction being highlighted, by the 
authors, is that there do exist members of the real numbers which have 
an infinite-length representation (for example, 1/3 in base 10), but 
that this will never be the case for any integer, supposing that they 
are represented without decimals (ie, 1.00000... is in the value space 
of integers, but is not a member of the lexical space for integer 1).

> I suspect the "finite length" verbiage is there to prevent someone
> from feeding a parser an unending stream of digits. It's not
> mathematically necessary.
Or indeed to imply the lemma that when _writing_ any integer, the 
process would halt in a finite number of steps.

Michael (and veering away from XSD):

> Perhaps the set of finite-length strings is itself infinite?
It will be, but since there are as many elements in that set as there 
are positive integers (they can be put into a one-to-one 
correspondence), it is no bigger or smaller an infinity than the number 
of integers.  In contrast, the number of real numbers is a 'larger 
infinity' than the number of integers.  If you wish to further explore 
this rabbit hole, see <https://en.wikipedia.org/wiki/Aleph_number> and 
work outwards...

Best wishes,

Norman


--
Norman Gray  :  https://nxg.me.uk