(November 3, 2011 at 12:18 am)IATIA Wrote: It is accepted because the definition of numbers requires a divisible space between each. Because there is no divisible space between 0.999... and 1, it is accepted as 1. The proofs, however, are all wrong. But we do not know what else to do with this number without shaking the foundations mathematics.
The proofs are correct. Any repeating decimal number is merely a representation of an exact rational number.