> 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.

How do I better understand that all integers have a finite number of 
digits, but there are infinite number of them? That's the bit I'm 
struggling with.

The way I see it, the number of positive integers with N or fewer digits 
is 10^N, so if N is finite then 10^N has got to be finite too?

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