Roo: The Rounding Operator - A Mathematical Paper

Abstract

This paper introduces Roo, a compact mathematical operator notation for rounding real numbers to a specified integer precision using the round-half-away-from-zero rule. The notation extends naturally to negative precision values, rounding to positions left of the decimal point, and is shown to be idempotent under repeated application at fixed precision. The paper also introduces Reb, the Roo Error Bound, and proves that the error introduced by rounding any real number is always bounded by one half of ten to the negative precision.