/sci/ - Science & Math

What do you mean actually equal, all operations are the result of definitions.

The latter.

well the gamma function of 1 is 1...

It's equal.

4! = 4 * 3 * 2 * 1 = 24
3! = 3 * 2 * 1 = 6

To get from 4! to 3!, you would need to divide 4! by 4 (which basically cancels out the 4). Continuing this pattern:

2! = 3!/3 = 6/2 = 2
1! = 2!/2 = 2/2 = 1
0! = 1!/1 = 1/1 = 1

1! =

It's both, dummy.

(n-1)! = n!/n

Therefore
0! = 1!/1
0! = 1

Yeah but like, does (-1/2)! really equal the square root of pi? o_o

http://en.wikipedia.org/wiki/Gamma_function

This is what you need to study.

>>3104583
>>3104573
That's not how recursive definitions work, you need to work off of a base case. Otherwise you have to find factorials out to infinity just to get 3!

n! = (n-1)! * n
0! = 1

Conceptually, imagine that you have 3 differently colored balls (red, blue, and yellow). In this case, 3! is the number of different ways you can arrange the balls:
RBY, RYB, BRY, BYR, YRB, YBR

2! is the number of ways you can arrange two balls:
RB, BR

1! is the number of ways you can arrange one ball:
R

0! is the number of ways you can arrange zero balls:
(nothing)

So you see, (nothing) is the only way to arrange zero balls, so 0! is equal to one.

>>3104595
this, niggers

WTF do you mean "actually equal"? There are no such two things defined to be equal that do not necessarily equal. So it's useless to discuss things that are ACTUALLY equal.

>>3104652
I mean, it's useless to discuss whether two things that are defined to be equal are actually equal.

>>3104629
Very helpful thanks.

Thanks for all the replies, guys. I'll look into the gamma function. Thanks for being helpful and resisting the urge to just make fun of me at what I assume is probably a pretty simple problem. I really appreciate it and wish you all well in your daily lives.

>>3104549
>Does the factorial 0! actually equal one or is it just defined as being so for functionality?
There's a difference?

>>3104556
got it right.
>What do you mean actually equal, all operations are the result of definitions.

I read this as "0 does not equal 1"

Fucking programming...

>>3104683
proof that CSfags cannot into math

My knowledge of math history isn't superb, but weren't factorials used before the gamma function was? I know the n! notation is relatively modern, but I'm pretty sure the use of factorials goes back hundreds and hundreds of years. People probably encountered 0! during that time, so I'd imagine it was defined to equal 1 before anyone even knew what the gamma function was.

I'm just saying this since I feel that saying that it equals BECAUSE of the gamma function is incorrect, but more that the gamma function agrees with the definition (as it should)

>>3104683
Same here, lol. I was like... well, I can't argue with that.

>>3104691
why don't you say that to my face not online and see what happens motherfucker

>>3104689
You are right.

>>3104697
>cannot into
wat

>>3104697
Middle school faggot detected

>>3104709
newfag detected

>>3104556
>>3104681
I'm sorry I worded my question very poorly and improperly, but fortunately for my sake people still understood what I meant. I was basically asking how 0!=1. I'm sorry for causing any unneeded confusion, but you are indeed correct.

Read into the gamma function and it's relation to factorials.

You can use the gamma to prove that 0!=1. I won't go into depth here, I was briefly taught it in elementary differential equations.

>>3104709

newfag detected.

>>3104729

oh fuck me, thats what I get for not reading the thread haha.

>>3104697
I have to agree with the comments about this post. This is a terribly immature thing to post on the internet.

>>3104750
Which is why it got turned into a meme

>>3104697
>>3104700
>>3104707
>>3104709
>>3104721
>>3104741
>>3104750
>>3104755

>>3104721
>>3104741
samefag detected

>>3104779

retard detected.

>>3104790
>>3104779

Guys come on I want to talk about the gamma function