Jacob (Jacques) Bernoulli

1. Law of Large Numbers

Bernoulli proved the first version of this fundamental probability theorem.

$$ \lim_{n \to \infty} P\left( \left| \frac{S_n}{n} - p \right| < \epsilon \right)=1 $$

2. Compound Interest Limit

The discovery of the constant \(e\).

$$ e = \lim_{n \to \infty} \left( 1 + \frac{1}{n} \right)^n $$