1=0.999…. A Formal Proof (Kind of)

In this article, I present a formal proof that the recurring decimal 0.999…. is in fact equal to 1. In doing so, however, I will sidestep a little of the more formal notation and strictness that a truly airtight proof would require. Instead, I will opt for presenting the main concepts required for the proof and show the construction of the proof based off these.

With this in mind, before we can begin the construction of our proof, we require the use of some techniques and ideas from a branch of mathematics known as real analysis. In particular, we first need to discuss…