3.999999............ isn't really a number. It's a bounded quantity. You can't really do arithmetic operations on bounded quantities like that. When you multiply by ten, you would be, in effect, terminating the decimal. Because the operation is illegal, multiplication by ten is only partly defined and doesn't really get you anywhere. This is really just a typical fallacy proof.

What it can be reduced to is the following:

4-3.999999...... = 0.0000000000000000000000.........

There are theoretically an infinite number of zeroes in the result, but logically it can never terminate. If it did terminate, it would violate the idea that it's a non-terminating, repeating decimal.

Really, is 1/inf = 0? It's an infintesimal, but it's not zero. It represents a nonzero quantity.

Edited on August 1, 2005, 3:22 pm

Posted by Eric on 2005-08-01 15:22:23