In
mathematics, the
repeating decimal 0.999… (sometimes written with more or fewer 9s before the final
ellipsis, for example as
0.9…, or in a variety of other variants such as
0.,
0.(9), or ) denotes a
real number that can be shown to be
the number one. In other words, the symbols "0.999…" and "1" represent the same number.
Proofs of this
equality have been formulated with varying degrees of
mathematical rigor, taking into account preferred development of the real numbers, background assumptions, historical context, and target audience.