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0! is defined as 1. QED.
I think you misunderstand the terms ' definition ' and 'prove'.
You can explain why it 'makes sense' it should be one, but when it comes down it it, it's just defined to be that.
everything has a prove in mathematics ,
http://en.wikipedia.org/wiki/Axiom . Now shut up please.
see, i can prove it but there is always some "bug". maybe it will work for you but for some other person (who has more knowledge of maths) can prove it wrong.
I mean, like I said there are EXPLANATIONS like this http://www.adonald.btinternet.co.uk/Factor/Zero.html But it is different.
prove it ,it does,nt mater ,it will add knowlede
its a convention
lots of math people got together and decided, hey this is going to be the way
but the reason for it , it simplifies many formulas
thanks ,newton it was helpful
so maybe you should ask, whats the reason for the convention, thats a better question,
it can be proved using Gamma function
its just a definition, so you cant ask to prove a definition
or simply using the definition of the n!
you cant prove for example, that a bachelor is unmarried. its a definition
"It can be proved using the definition" Hmm, sounds like a proof to me (xD)
well n! = n * n-1 *...*3*2*1
theres isnt 0! in it
i am on my phone so its hard for me to type the whole derivation. or i would have given you
proof, by definition? ok i guess
but we dont define things just willy nilly. they are usually well good god reasons for it
n!=n(n-1! put n=1
While you're at it, prove all the axioms please, umza? And (technically), \[1! = 1 \times 0! \] \[2! = 2 \times 1! \] \[3! = 3 \times 2! \] ... \[n! = n \times (n-1)! \]
Umza please go learn the definition of 'proof' and come back.
uzma, that doesnt work
ok thank u
uzma , what about 0! = 0 * (0-1)! ?
anyways, i like the binomial series , i think its called pochhammer
(0-1)! does it work?
the reason why we have 0! is because we have n choose r = n! / ( n-r)! r!
and when you have r = 0, we have n! / n! 0!
the actual proof is done using Gamma function
wait, its false that 0! = 0 * (0-1)!
the proof for what, the bionomial series
oh sorry, i misread the question and thought that you are asking to prove 0 = 1 instead of 0! = 1 lol. its very easy to prove.
OMG yes it's SOOOO EASY to prove - just do it quickly please?
but i don't know to type, its not easy to type "please".
Oh, I thought so.
i'm back!!! are you guys there. lol