I was just discussing this very issue with my good friends JB, Ben, James, and Chuck over some tasty La Pizza pizza.
Proof that 0.999… equals 1
From Wikipedia, the free encyclopedia
The recurring decimal 0.999… equals 1, not approximately but exactly. More precisely, the standard real number represented by 0.999… (where the 9s repeat forever) is exactly equal to the standard real number 1.
Proofs of this equality vary depending on the level of rigor demanded and on what results are assumed to be already known. All proofs rely on properties of the standard real numbers. There are other so called “non-standard” real numbers, for which the equality does not hold. In many of these number systems, 0.999… is not well-defined.