Factorials

Why is $0!$ equals to $1$ ?

I cannot understand.

#Calculus

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

Factorials have one general property, $\frac{x!}{x}=(x-1)!$ Using this on $x=1$

We have : $\frac{1!}{1}=0!$ $1=0!$

Jason Gomez - 3 months, 3 weeks ago

Another reason uses a combinatorial argument that the number of ways of choosing 2 things from 2 things is one

And that should be equal to $^2C_2=\frac{2!}{2!×0!}$ , which directly results in $0!=1$

Jason Gomez - 3 months, 3 weeks ago

Is like you said a initial question or condition if I have a number n, how many initial is the combination? Like 1 is 1, “0” combination is 1 for only “0”

Elijah Frank - 3 months, 2 weeks ago

Could you state your statements a little more clearly, I am not able to understand what you are trying to tell me

Jason Gomez - 3 months, 2 weeks ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$