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Re: [xml-dev] Infinity
• From: "Norman Gray" <norman@astro.gla.ac.uk>
• To: "Elliotte Rusty Harold" <elharo@ibiblio.org>
• Date: Sat, 03 Mar 2018 13:33:19 +0000

```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

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