0! = 1

No matter how many times someone tries to explain it to me, I can never understand it.

/sci/ halp plz?

http://mathforum.org/library/drmath/view/57905.html

>>1
It was originally a convention I believe because it was useful for certain forumalae. Mathematicians now just define factorials as (n-1)! = (n!/n) and it makes sense.

Gamma function lol.

>>4
>>4
>>4
>>4

>>4
hmmm... i see

"The factorial function is a special case of the gamma function."

>>4
The invention of the gamma function must've been hilarious.
"Wow, guys, thank god we have a notation for the factorial, eh? Now we don't have to write anything out anym—"
"Hey, what if we want to take the factorial of a fraction?"
"..."
"..."
"...fuck"

>>1
The factorial is mostly used by statisticians anyway, and they don't care about mathematical reasons.

I'm not sure if this is correct, but I've always thought about it this way:

3!x = 1*2*3*x
2!x = 1*2*x
1!x = 1*x
0!x = x

RON PAUL /sci/,

I have discovered an amazing site. Turn the volume for your computer ON, and go to http://blocked.on.nimp.org with Internet Explorer. After going there with Internet Explorer, go there with Mozilla Firefox.

>>8
Any field of "math"/science that takes a square root and completely disregards the negative result doesn't care about mathematical reason. Just results.
I'm looking at you, physfags. Can't have negative length? Pfft.

RON PAUL /sci/,

I have discovered an amazing site. Turn the volume for your computer ON, and go to http://blocked.on.nimp.org with Internet Explorer. After going there with Internet Explorer, go there with Mozilla Firefox.

>>11
Basil?

Oregano?

>>13
lolwut?

fac 0 = 1
fac n = n * fac n-1

It's just part of the definition, there's nothing to understand really. The gamma-function is a nice generalization, but the factorial would still be the factorial without it.

0! is the product of no numbers at all, and the product of no numbers is 1 since 1 is the identity element for multiplication.

>>17
That's what I was trying to get at in >>9

>>18
Even though you basically just said 0!=1 and didn't answer the original question anyway.

0 != 1

fixd

>>19
Read it again.  How is it not a decent illustration of your answer?  The factorial is multiplied by an unknown constant, then it breaks up into each number from the factorial times the constant.  In the final example you have the constant but don't multiply it by anything as there are no numbers with which to do so.  It would have made slightly more sense just use 1 instead of x, but it gets the message across nonetheless.

>>11

Measure is always greater or equal to zero in math, too.

>>20
WIN

>>20
>>23
samefag

>>21
See the thing is x = 1*x. So it's not a good illustration at all.

I like the (n-1)! = (n!/n) definition. But anyway the function is defined as it is and is useful. All that matters.

i asked this in /b/ and a few people explained it well for me.

here're the responses i got:

EXPLANATION 1

If you have zero objects, you can only arrange them in one way.

EXPLANATION 2

    imagine that instead of thinking of 3!=1*2*3 think of it as 1*2*3*4/4

    1!=1*2/2

    so 0!=1/1

EXPLANATION 3

"Experimenting with factorials, we come up with n!=n(n-1)!. For example 17!=17x(16!):

16!=1x2x...x16
17!=(1x2x...x16)x17

That equation (n!=n(n-1)!) just dictated to us where to put the parentheses. By making n=1, we can find 0!:

1!=1(0!)
0!=1

And, it turns out that 0!=1 works very well in many situations (in probability, for example)."

EXPLANATION 4

    Look up the gamma function. G(n) = (n-1)!. The gamma function evaluates to 1 at 1. This definition just makes sense and makes combinatorics less messy.

EXPLANATION 5

    There is NO way to explain this.
    If this fact is accepted as true, then other formulas work. No evidence of this fact exist.

Jesus, hasn't anybody here ever heard of the empty product?  The product of zero things is the multiplicative identity (1), just like the sum of zero things is the additive identity (0).