1. The problem is to understand the mathematical constant $e$. 2. The number $e$ is an irrational and transcendental constant approximately equal to 2.71828. 3. It is defined as the limit: $$e = \lim_{n \to \infty} \left(1 + \frac{1}{n}\right)^n$$ 4. Another important definition is through the exponential function: $$e^x = \sum_{n=0}^\infty \frac{x^n}{n!}$$ 5. The constant $e$ is the base of natural logarithms, meaning: $$\ln(e) = 1$$ 6. It appears frequently in calculus, especially in problems involving growth and decay, compound interest, and differential equations. 7. Understanding $e$ helps in solving problems involving continuous growth or decay processes. Final answer: $e \approx 2.71828$