Stemming from an idea put forward by Loo-Keng Hua in 1962, this article describes an original way to perform arithmetic directly on infinite decimals. This approach leads to a new and elementary construction of the real number system via decimal representation. Based on the least upper bound property, a definition of trigonometric functions is also included, which settles an issue that Godfrey H. Hardy called \a fatal defect" in his Course of Pure Mathematics.
Fardin, Nicolas and Li, Liangpan
"Real numbers as infinite decimals,"
The Mathematics Enthusiast: Vol. 18
, Article 4.
Available at: https://scholarworks.umt.edu/tme/vol18/iss1/4