0!= 1 ?!

[Tnad]

Can you explain how?

how can 0!=1 and 1!=1

Thanx

[the tree]

Intuitively: how many ways do think there are to order zero objects?

 

Slightly less intuitively:

[math]n! = n (n-1)![/math]

 

[math]1! = 1 \cdot 0![/math]

 

[math]0! = \tfrac{1!}{1} = 1[/math]

 

Really: that's just the definition.

[Tnad]

Thank you, the tree.

I get it now.

[the tree]

Oh I just thought, it's worth mentioning that the factorial function can be generalised to the Gamma function.

 

[imath]n! = \Gamma(n+1)[/imath] where [imath]\Gamma(z) := \int_0^\infty t^{z-1} e^{-t}\,dt[/imath].

 

And you should be able to verify that [imath]\Gamma(1)=\Gamma(2)=1[/imath] if you're okay with integration by parts.

[Tnad]

Right.I'm okey with integration by parts but I didn't know about the extension of the factorial function.Thanx,again!