How

>>8517674
I know it's bait, but I'll bite. There are algebraic ways to explain it, but what about this way?

3! Is how many different ways you can permute 3 things. 6 ways.
2! Is how many ways you can permute 2 things, and so forth.
Now, how many ways can you permute 0 things?

>>8517685
0?

>>8517674
n! = (n+1)!/(n+1) for all n.

So :

0! = (0+1)!/(0+1) = 1!/1 = 1

>>8517691
Nope, there is one and only one way to sort zero things. I'll show you:

See?

P(1,1)=1/0!=1 obv

>>8517674
10^6=1000000-->/10
10^5=100000-->/10
10^4=10000-->/10
10^3=1000-->/10
10^2=100-->/10
10^1=10-->/10
10^0=1-->*/10
10^-1=0.1-->*10
10^-2=0.01-->*10
10^-3=0.001-->*10
10^-4=0.0001-->*10
10^-5=0.00001-->*10
10^-6=0.000001-->*10

Becouse
[math]n!=\Gamma(n+1)=\int_0^\infty x^n e^{-x} dx[/math]

5! = 5×4×3×2×1×1
4! = 4×3×2×1×1
3! = 3×2×1×1
2! = 2×1×1
1! = 1×1
0! = 1

because it's easier that way

>>8517674
n! = n * (n-1)!
1! = 1
1! = 1 * 0!
1 = 1 * 0!
1 = 0!

>>8517674

Because the exclamation point means the zero is shouting and being confident upgrades it to the number one.

>>8517674

Numberphile did a video on it, go check it out.

File: e9b14930c230c43bb598ab17dd2b51f8.png (14KB, 651x421px) Image search: [Google]

14KB, 651x421px

Riddle me this, /sci/

>>8518046
0! = 1 = 0 * (-1)!

yes verry nice

>>8518075
[math]\Gamma (z)=\int _{0}^{\infty }t^{z-1}e^{-t}\,\mathrm {d} t.\![/math] and [math]n!=\Gamma (n+1).\,[/math]