Let $k$ be a field with multiplicative identity $1_k$ and additive identity $0_k$, and let $\mathbb{N}=\{1,2,3,\dots\}$. Define $\operatorname{char}(k)=0$ if there is no $m\in\mathbb{N}$ such that $m\cdot 1_k=0_k$; otherwise define $\operatorname{char}(k)$ to be the least $n\in\mathbb{N}$ such that $n\cdot 1_k=0_k$. Then $\operatorname{char}(k)=0$ or there exists a prime number $p$ such that $\operatorname{char}(k)=p$.