The Factorial: The Most Useful Idea in Mathematics

The factorial is one of the most elegant ideas in all of mathematics.

It starts with a simple question: How many ways can you arrange 3 books on a shelf?

But this simple concept reaches into:
Probability — calculating your lottery odds
Computer Science — why some problems are "impossible" to solve
Physics — how infinite series converge
Pure Mathematics — unexpected connections to π

From counting arrangements to the edges of mathematical infinity — this is the factorial.

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⏱️ TIMESTAMPS:
0:00 - Introduction
0:30 - A Simple Question (3 Books)
0:42 - Counting Step by Step
1:05 - All Six Arrangements
1:28 - The Formal Definition
2:14 - Explosive Growth
3:05 - Probability: Permutations
4:11 - Combinations & Lottery Odds
4:51 - Computer Science: Traveling Salesman
6:06 - Physics: Taylor Series
7:26 - The Gamma Function (½! = ?)
8:41 - Summary
9:02 - Closing

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