Math Question: Factorial

[Safeway]

Definition: (Mathematics) The product of a given positive integer multiplied by all lesser positive integers: The quantity four factorial (4!) = 4 · 3 · 2 · 1 = 24. Symbol: n!, where n is the given integer.

5! = 5 x 4 x 3 x 2 x 1 = 120
4! = 4 x 3 x 2 x 1 = 24
3! = 3 x 2 x 1 = 6
2! = 2 x 1 = 2
1! = 1 = 1

...

Why the fvck does 0! = 1?

 

[HN]

It's simple, really: http://www.adonald.btinternet.co.uk/Factor/Zero.html

















😕

 

[Matthias99]

By definition.

No, seriously, it's just defined that way. It does make some other things related to factorials work more nicely (like some of the probability equations).

http://mathforum.org/library/drmath/view/57128.html

 

[George P Burdell]

By definition.

 

[Cooler]

Its because its a base case!

 

[blackllotus]

Originally posted by: HN
It's simple, really: http://www.adonald.btinternet.co.uk/Factor/Zero.html

That explanation is wrong. You can only divide by n on both sides if n != 0. If it equals zero then the results are undefined so that proof is invalid.

 

[Safeway]

I am not disputing that it is true, I have taken and passed Differential Equations, Partial Differential Equations, Vector Cal, ... but I never understood why 0! = 1. It just seems lame.

 

[chuckywang]

Look up the "Gamma function."

 

[Tiamat]

Originally posted by: chuckywang
Look up the "Gamma function."

I was just about to say this.

like, where the fvck does PI come into play for non-integer factorials!!

 

[Jeff7]

Originally posted by: Safeway
I am not disputing that it is true, I have taken and passed Differential Equations, Partial Differential Equations, Vector Cal, ... but I never understood why 0! = 1. It just seems lame.

I was confused in Calc II by something weird - the area underneath a curve was found by definite integral to be infinite. Then that area was revolved around the x-axis. Its volume was pi. Somehow, a rough cylinder with infinite length had a volume of pi. Made no sense, but it was checked as being correct.

 

[mugs]

Originally posted by: HN
It's simple, really: http://www.adonald.btinternet.co.uk/Factor/Zero.html

















😕

Long story short:

n! = n * (n-1)!

So
1! = 1 * (1-1)!

1! = 1, so (1-1)! must be 1 otherwise that equation wouldn't be equal.

 

[Safeway]

Originally posted by: Jeff7

Originally posted by: Safeway
I am not disputing that it is true, I have taken and passed Differential Equations, Partial Differential Equations, Vector Cal, ... but I never understood why 0! = 1. It just seems lame.

I was confused in Calc II by something weird - the area underneath a curve was found by definite integral to be infinite. Then that area was revolved around the x-axis. Its volume was pi. Somehow, a rough cylinder with infinite length had a volume of pi. Made no sense, but it was checked as being correct.

I was caught up in the same crap too. A lot of mathematics does against common sense.