Quote:
Originally Posted by shendo
.999~ is not a limit. it IS an infinite number of 9's.
we do agree that the different is infinitely small, in that its 1/oo. of course 1/oo = 0.

Fwiw 1/infinity isn't necessarily defined as 0 since the extended real number system isn't a field. Thus we can't do algebraic things involving it and have them be necessarily accurate.
We can however say that the limit of 1/x as x approaches infinity = 0.
Also, how about this for a mind blower for people:
Georg cantor came up with this many years ago, it's a proof of the uncountability of real numbers and is the basis for set theory/cardinality.
Form a set of all infinite decimal expansion real numbers between 0 and 1. Now, take the (1,1) first number of first line and (2,2), (3,3), etc for all numbers in the set. For this new decimal between 0 and 1, change every digit from whatever it is to anything else. Now, this number we have created is different from every number in the set previously, and thus we can add it to the set as a "new number". However, we can do this infinitely many times. Thus the real number system is infinitely dense.
So, we have an infinite decimal expansion with infinite separate numbers in between 0 and 1, and infinitely many spaces = to the difference between 0 and 1 in the set of all real numbers.