Manjul Bhargava defined the concept of a $p$-ordering of a subset of a Dedekind ring, where $p$ is a prime. In the case of $S\subseteq \mathbb{Z}$, the definition is as follows. Let $a_0\in S$ be arbitrary, and for $i>0$, let $a_i$ be any element of $S$ that minimizes the highest power of $p$ dividing $$(a_i - a_0)(a_i - a_1) \cdots (a_i - a_{i-1}).$$ Stating this definition almost automatically prompts us to examine the sequence of highest powers that arise, and the fundamental theorem of the subject is that this sequence of highest powers is independent of the choice of $p$-ordering. This theorem quickly led to huge progress on some long-standing and difficult questions about polynomial mappings on subsets of $\mathbb{Z}/n\mathbb{Z}$, and also led to a generalized notion of factorials whose theory is an ongoing topic of research.