0!

[ResidentIdiot]

Why does 0!=1

 

[heliomphalodon]

There are several reasons.
First, 0! is defined as 1 so that certain combinatorial formulas will have simple forms.
Second, the factorial function can be extended from the integers to the entire complex plane by use of the gamma function. As I recall, this leads to a definition of z! = gamma(z+1) for all complex z (except for z=0, -1, -2, -3,...). Since gamma(1)=gamma(2)=1 we have 0!=1.

 

[ResidentIdiot]

Gr8 thanks.

 

[MrDudeMan]

Originally posted by: heliomphalodon
There are several reasons.
First, 0! is defined as 1 so that certain combinatorial formulas will have simple forms.
Second, the factorial function can be extended from the integers to the entire complex plane by use of the gamma function. As I recall, this leads to a definition of z! = gamma(z+1) for all complex z (except for z=0, -1, -2, -3,...). Since gamma(1)=gamma(2)=1 we have 0!=1.

wow

 

[OrionAntares]

Originally posted by: MrDudeMan

Originally posted by: heliomphalodon
There are several reasons.
First, 0! is defined as 1 so that certain combinatorial formulas will have simple forms.
Second, the factorial function can be extended from the integers to the entire complex plane by use of the gamma function. As I recall, this leads to a definition of z! = gamma(z+1) for all complex z (except for z=0, -1, -2, -3,...). Since gamma(1)=gamma(2)=1 we have 0!=1.

wow

I second that.

 

[stebesplace]

my brain is fried

 

[RemyCanad]

All I can say is this is why I like the Highly Technical Forum.

Also great answer heliomphalodon.

 

[KillerCow]

Originally posted by: heliomphalodon
There are several reasons.
First, 0! is defined as 1 so that certain combinatorial formulas will have simple forms.
Second, the factorial function can be extended from the integers to the entire complex plane by use of the gamma function. As I recall, this leads to a definition of z! = gamma(z+1) for all complex z (except for z=0, -1, -2, -3,...). Since gamma(1)=gamma(2)=1 we have 0!=1.

I would add to that a simpler reason... factorial represents the number of times that a set of size n can be permuted.

A set of 0 things has 1 permutation... the permutation of nothing.

so 0! = 1

see: Factorial

 

[heliomphalodon]

Originally posted by: KillerCow
A set of 0 things has 1 permutation... the permutation of nothing.

so 0! = 1

With all due respect, I don't think that helps -- one could just as sensibly say that the empty set has zero permutations.

 

[ResidentIdiot]

It's ok guy's I just did my maths exam and they didn't ask me about it. Got to do electronics and statics now 🙁

 

[KillerCow]

With all due respect, I don't think that helps -- one could just as sensibly say that the empty set has zero permutations.

No, it has one: the empty set.

 

[Peter]

Originally posted by: KillerCow

With all due respect, I don't think that helps -- one could just as sensibly say that the empty set has zero permutations.

No, it has one: the empty set.

Right ... as soon as we agree that an empty set is something that exists, it has one state of existence, one permutation.

 

[Smilin]

Originally posted by: heliomphalodon
There are several reasons.
First, 0! is defined as 1 so that certain combinatorial formulas will have simple forms.
Second, the factorial function can be extended from the integers to the entire complex plane by use of the gamma function. As I recall, this leads to a definition of z! = gamma(z+1) for all complex z (except for z=0, -1, -2, -3,...). Since gamma(1)=gamma(2)=1 we have 0!=1.

For some odd reason when I read the above, my liver busted. The pain has subsided now though and I think I'm going to pull through. This has never happened before.

Strange.

 

[LordMagnusKain]

zero isn't real, becase if zero whe real, nothing would exist 🙂

 

[silverpig]

Originally posted by: KillerCow

With all due respect, I don't think that helps -- one could just as sensibly say that the empty set has zero permutations.

No, it has one: the empty set.

0 = {}
1 = {0}
2 = {0,1}

So 1 has 1 permutation, {0}. 0 has 0 permutations {}...

 

[Peter]

Sure, you cannot rearrange nothing, but neither can you rearrange one thing. Yet still you can HAVE one thing or nothing. There is one state of having nothing. 0!=1.