On 7/16/2013 12:35 AM, scott wrote:
>> Integers are allowed to have infinite digits before the decimal place.
>> Reals are allowed them after the decimal place as well. ;-)
>
> Genuine question then, why isn't the set of real numbers countable,
> given that you could represent each one with two integers (one for the
> digits before the decimal point, one for the digits after the decimal
> point)?

I didn't comment on Orchid's quip since I assume he was joking, but you 
are rightly confused because it is completely incorrect.  Real numbers 
do indeed have an "integer before the decimal place", but critically 
*not* necessarily "after the decimal place".  The reason is that there 
may be infinitely many digits after the decimal place, all integers only 
have a finite number of digits.

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