1. **Problem Statement:** Understand the mathematical constant $e$ and its value. 2. **Definition:** The number $e$ is a fundamental mathematical constant known as Euler's number. 3. **Value:** It is an irrational number approximately equal to $2.71828$. 4. **Importance:** $e$ is the base of natural logarithms and appears frequently in calculus, compound interest, probability, and many areas of mathematics. 5. **Mathematical Expression:** It can be defined as the limit: $$e = \lim_{n \to \infty} \left(1 + \frac{1}{n}\right)^n$$ 6. **Explanation:** This means as $n$ becomes very large, the expression approaches $e$. 7. **Summary:** $e$ is approximately $2.71828$ and is essential in continuous growth and decay models, among other applications.