To begin with, the decimal representation of real numbers is not unique. To see this consider

I claim thata=0.99999...

To see this note thata=1

10a = 9.99999... a = 0.99999... (subtract) ---------------- 9a = 9 ==> a = 1

In general, there are real numbers that can be expressed
either as a number ending in an infinite string of nines or
an infinite string of zeros. That's the only way the real
representations are not unique! (Proving this is a good **
exercise** ). To obtain a unique decimal representation
of a real number we usually impose the convention that it
not end in an infinite string of nines.

Fine print, your comments, more links, Peter Alfeld, PA1UM

[16-Aug-1996]