> Note that an infinite string of digits does not represent an integer
> (because no integer is infinite.) That's probably what causes the
> confusion.

True.

> ("No real number is infinite either." That's correct. But the decimal
> representation of a real number can be.)

That also probably explains why you can't represent every real number 
with two integers (one for the fractional part and one for the integral 
part).

>> Because you can do a similar thing with a list of all
>> natural numbers, ie calculate the sum and then you get a new natural
>> number that wasn;t in the list to start with.
>
> You cannot sum all the natural numbers because there's an infinite
> amount of them.

I guess the bit I got confused with / didn't understand is that you can 
have a set with an infinite number of natural numbers, yet none of the 
natural numbers themselves are infinite in size.

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