.999 Repeating Equals 1

Does .999... (repeating) actually equal 1? Without any rounding, it can be proven that .999... in fact does equal 1.

Consider the following proof.

1/3 = .333... (The repeating value .333... is the result of 1 divided by 3.)

Written as fractions, 3 x 1/3 can also be written as (3/1) x (1/3), which equals 1. However, when the same equation is written in decimal form, 3 x .333... equals .999...

Therefore, (3 x 1/3) and (3 x .333...), is the same as 3/3 (or 1) = .999...

I ask that the math wizards forgive my sloppy style of proving this.