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# Lesson 7.4: Factorial

## Symbols

$!\phantom{\rule{.3em}{0ex}}\text{factorial symbol}$

## Explanation

A factorial is a mathematical progression that is calculated by multiplying an integer and all the integers below it. The factorial symbol is the exclamation point. The braille exclamation point is used in keeping with the UEB principle that each print symbol has one and only one braille equivalent.

### Example 1

$4!$
⠼⠙⠖

### Example 2

$3!=3·2·1$
⠼⠉⠖⠀⠐⠶⠀⠼⠉⠐⠲⠼⠃⠐⠲⠼⠁

### Example 3

$4!=1×2×3×4$
⠼⠙⠖⠀⠐⠶⠀⠼⠁⠐⠦⠼⠃⠐⠦⠼⠉⠐⠦⠼⠙

### Example 4

$\frac{4!}{3!}$
⠰⠷⠼⠙⠖⠨⠌⠼⠉⠖⠾

### Example 5

$\frac{n!}{\left(n!+x\right)!}$
⠰⠰⠷⠝⠖⠨⠌⠐⠣⠝⠖⠐⠖⠭⠐⠜⠖⠾