Working with the set of real numbers

[Chris Angelico]

On Wed, Feb 12, 2014 at 9:07 PM, Ben Finney <ben+python at benfinney.id.au> wrote:
> Chris Angelico <rosuav at gmail.com> writes:
>
>> On Wed, Feb 12, 2014 at 7:56 PM, Ben Finney <ben+python at benfinney.id.au> wrote:
>> > So, if I understand you right, you want to say that you've not found
>> > a computer that works with the *complete* set of real numbers. Yes?
>>
>> Correct. […] My point is that computers *do not* work with real
>> numbers, but only ever with some subset thereof […]
>
> You've done it again: by saying that “computers *do not* work with real
> numbers”, that if I find a real number – e.g. the number 4 – your
> position is that, since it's a real number, computers don't work with
> that number.
>
> That's why I think you need to be clear that your point isn't “computers
> don't work with real numbers”, but rather “computers work only with a
> limited subset of real numbers”.

Hmm, I'm not sure that my statement is false. If a computer can work
with "real numbers", then I would expect it to be able to work with
any real number. In C, I can declare an 'int' variable, which can hold
the real number 4 - does that mean that that variable stores real
numbers? No, and it's not useful to say that it does. It doesn't store
rationals either, even though 4 is a rational. The fact that computers
can work with some subset of real numbers does not disprove my
statement that computers don't work with "real numbers" as a class.
Program X works with text files, but it fails if the file contains
U+003C; can I feed it this thing, which is a text file? No, I can't,
because it works only with a subset of text files.

ChrisA