Limit Comparison Test Defined entirely in symbolic notation Is it possible to define the limit comparison test entirely with symbols (no textual explanation), or with as little textual explanation as possible? How? My latest best attempt: $0<\lim_{n\to\infty}\frac{a_n}{b_n}<\infty\implies \sum{a_n}=\infty(XOR)\sum{b_n}=\infty$

With your assistance, and this was alot of fun,

$$\left(0<\lim_{n\to\infty}\frac{a_n}{b_n}<\infty\right)\Rightarrow \left(\sum{a_n}=\pm\infty\wedge\sum{b_n}=\pm\infty \right)\vee \left(\sum{a_n}\in\mathbb{R}\wedge\sum{b_n}\in\mathbb{R} \right).$$