1. The symbol $\infty$ represents infinity, which is not a number but a concept describing something without bound or limit. 2. Infinity is used in mathematics to describe limits, unbounded growth, or sizes of sets. 3. It is important to note that operations involving infinity follow special rules, for example, $\infty + a = \infty$ for any finite number $a$, and $\infty \times a = \infty$ if $a > 0$. 4. Infinity is not a real number and cannot be treated as one in algebraic operations. 5. In calculus, limits involving infinity help describe behavior of functions as inputs grow very large or very small. 6. Thus, $\infty$ is a useful concept but must be handled carefully according to mathematical context.