Why is 0! = 1? (1 Viewer)

[Famine]

Im here working through the binomial theorem, and I come across 0! (zero to the factorial) is equal to 1. Just curious, how is this so? I just cant comprehend how it could equal anything other than 0.

 

[Stefano]

0! = 1 by definition. Don't get a headache trying to imagine it

 

[serge]

Im here working through the binomial theorem, and I come across 0! (zero to the factorial) is equal to 1. Just curious, how is this so? I just cant comprehend how it could equal anything other than 0.

its probably a problem created by the fact nCo=1

eg. 1c0= 1 in the other form 1!/ [0!(1)!] since that MUST=1

0! must= 1 aswell

 

[klaw]

n!=n*(n-1)!
.:n!/n=(n-1)!

When n=1, RHS=0! LHS=1
.:0!=1

 

[MAICHI]

Yes, it's very strange, never thought about that before. I think it's because factorial is used mostly in permutation so you define it in terms of permutation. For example, what is the permutation of zero things? 1 way of doing it right?

 

[Famine]

its probably a problem created by the fact nCo=1

eg. 1c0= 1 in the other form 1!/ [0!(1)!] since that MUST=1

0! must= 1 aswell

Yeah, thats the exact instance I am looking at. Oh well, I will just have to accept it then haha.

edit: good point MAICHI

 

[rama_v]

http://community.boredofstudies.org/showthread.php?t=71906

 

[Stefano]

Yes, it's very strange, never thought about that before. I think it's because factorial is used mostly in permutation so you define it in terms of permutation. For example, what is the permutation of zero things? 1 way of doing it right?

The permutation of zero is 0? Since there are no things to permute...
Depends on the type of 0.

perm. of zero thing = 0
perm. of zero things = 0! = 0+1 = 2-1 = 2/2 = (0/0)! = e⁰

EDIT: Ignore (0/0)!

 

[Famine]

The permutation of zero is 0? Since there are no things to permute...
Depends on the type of 0.

perm. of zero thing = 0
perm. of zero things = 0! = 0+1 = 2-1 = 2/2 = (0/0)! = e⁰

but (0/0) does not equal 1, as it is not a finite number

 

[MAICHI]

n!=n*(n-1)!
.:n!/n=(n-1)!

When n=0, RHS=0! LHS=1
.:0!=1

Works fine. But I think you meant n=1.

Stefano, in how many ways can we do nothing? 1 isn't it? I know it's a bit abstract.

 

[Stefano]

Haha, yes. But you get my point?

PS. Next time give me a chance to edit

 

[Stefano]

Stefano, in how many ways can we do nothing? 1 isn't it? I know it's a bit abstract.

I would of thought the answer would be either:

1. 0
2. Infinite
3. Something in between the last two.

Correct me if I'm wrong ?

 

[Slidey]

n!=n*(n-1)!
.:n!/n=(n-1)!

When n=1, RHS=0! LHS=1
.:0!=1

That is not a proof. There is no proof. It is a definition.

 

[Stefano]

That is not a proof. There is no proof. It is a definition.

That's what I said!


Pfft... just coz Slidey has a yellow name these days...

 

[Slidey]

"Because the number of permutations of 0 elements is 1, (zero factorial) is defined as 1 (Wells 1986, p. 31). This definition is useful in expressing many mathematical identities in simple form."

- Wolfram's MathWorld

 

[MAICHI]

I would of thought the answer would be either:

1. 0
2. Infinite
3. Something in between the last two.

Correct me if I'm wrong ?

For example, if I have 1 apple and 1 banana, how many ways can I eat them. I can eat the banana first then the apple, or I can eat the apple first then the banana. Hence there are 2 ways.

Now I only have a banana, how many ways can I eat this? I can only eat the banana, so 1 way.

Now imagine I want to eat nothing, how many ways can I eat nothing? 1 way right? It can't be 0 because that would mean I can NOT eat nothing!!

 

[Stefano]

For example, if I have 1 apple and 1 banana, how many ways can I eat them. I can eat the banana first then the apple, or I can eat the apple first then the banana. Hence there are 2 ways.

Now I only have a banana, how many ways can I eat this? I can only eat the banana, so 1 way.

Now imagine I want to eat nothing, how many ways can I eat nothing? 1 way right? It can't be 0 because that would mean I can NOT eat nothing!!

So I was correct!

PS. Nicely explained.

 

[Slidey]

For example, if I have 1 apple and 1 banana, how many ways can I eat them. I can eat the banana first then the apple, or I can eat the apple first then the banana. Hence there are 2 ways.

Now I only have a banana, how many ways can I eat this? I can only eat the banana, so 1 way.

Now imagine I want to eat nothing, how many ways can I eat nothing? 1 way right? It can't be 0 because that would mean I can NOT eat nothing!!

Next time you plan on eating nothing, tell me. I'd like to see it.

 

[Stefano]

Next time you plan on eating nothing, tell me. I'd like to see it.

Last time I drank nothing was when I drank 'Nuka Cola'.

 

[r.haidar]

For example, if I have 1 apple and 1 banana, how many ways can I eat them. I can eat the banana first then the apple, or I can eat the apple first then the banana. Hence there are 2 ways.

Now I only have a banana, how many ways can I eat this? I can only eat the banana, so 1 way.

Now imagine I want to eat nothing, how many ways can I eat nothing? 1 way right? It can't be 0 because that would mean I can NOT eat nothing!!

thats actually a really good way of thinking of it... lets say u have nothing... thats still something... its 1 thing... its 1 of "nothing"... get it ? lol its a hard concept... and u should probably post in 4u "extra cirricular maths" because the people there are really smart at deriving thigs... they prove shit like 1+1=2 and:

( a + b ) + c = a + ( b + c )

so go there n ask otherwise just accept it haha