For those interested, there's a nice exposition that treats real numbers as infinite decimals in Hubbard and Hubbard's <i>Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach</i> [1]<p>[1] <a href="http://matrixeditions.com/5thUnifiedApproach.html" rel="nofollow">http://matrixeditions.com/5thUnifiedApproach.html</a>