1. The problem is to understand the mathematical constant $e$. 2. The number $e$ is an irrational constant approximately equal to 2.71828. 3. It is the base of natural logarithms and appears in many areas of mathematics, especially calculus. 4. One way to define $e$ is by the limit: $$e = \lim_{n \to \infty} \left(1 + \frac{1}{n}\right)^n$$ 5. This means as $n$ becomes very large, the expression $\left(1 + \frac{1}{n}\right)^n$ gets closer and closer to $e$. 6. Another important property is that the function $f(x) = e^x$ has the unique property that its derivative is itself: $$\frac{d}{dx} e^x = e^x$$ 7. This makes $e$ fundamental in growth and decay problems, compound interest, and many natural processes. 8. In summary, $e$ is a special number that helps us understand continuous growth and change in mathematics.