/sci/ - Science & Math

[Anonymous No.2505489]

Pic is related
So /sci/ why it does?

[Anonymous No.2505518]

<span class="math"> 0!\equiv 1 [/spoiler]

[Anonymous No.2505544]

3! = 4!/4
2! = 3!/3
1! = 2!/2
0! = 1!/1 = 1

[Anonymous No.2505547]

>>2505518
asshole.

It is beacause
\frac{n!}{n} = (n-1)!
If we substitute n for 1, we'll have 1 = 0!

[Anonymous No.2505557]

>>2505547
<span class="math">\frac{n!}{n} = (n-1)! [/spoiler]

[Anonymous No.2505570]

>>2505557
>Division by zero

[Anonymous No.2505574]

>>2505570

n = 1 rtard.

[Anonymous No.2505576]

>>2505570
For n=0, yeah. So? n=1 is what gives you 0!.

[Anonymous No.2505580]

>>2505544
-1!=0!/0=what is this shit

[Anonymous No.2505594]

>>2505580
>factorial of a negative number
see, thats where you are going wrong

[Anonymous No.2505603]

it's called the empty product. same as how x^0 = 1 (when x =/= 0)

just as an empty sum adds up to 0 (the additive identity)

empty product multiplies to 1 (multiplicative identity)

[Anonymous No.2505611]

What was the general function that passes through all the same points as the factorial, but is also defined for non-integers?

Oh, I remember! The Gamma function!
http://en.wikipedia.org/wiki/Gamma_function

[Anonymous No.2505610]

because gamma function

[Anonγmous No.2505618]

>0!=1
Really? I think I'll google it

>Second result is the wiki entry for mathematical fallacy, but the article doesn't mention this example
I knew this sounded fishy.

>http://www.wolframalpha.com/input/?i=0!
Welp, time to sign myself up for more math courses so I can figure this shit out. What level of mathematics covers this craziness?

[Anonymous No.2505627]

>>2505603
this is a mystery for me to, why something^0 equal 1?

[Anonymous No.2505645]

>>2505627
it's pretty easy to understand

so a^b=a*a*a... b times right?
so a^(b-1)=a*a*a b-1 times, in other words, a^(b-1)=(a^b)/a
so lets say we have a^1=a
a^0=a^(1-1)=a^1/a=a/a=1

[Anonymous No.2505661]

>>2505645
This is why I love /sci/ so much :)
Thank you!

[Anonymous No.2505687]

all has to do with gamma functions like >>2505610
said.
not exactly sure how but i know it does!
http://en.wikipedia.org/wiki/Gamma_function

[Anonymous No.2505712]

<span class="math">0^0=1[/spoiler]

[Anonymous No.2505728]

<span class="math">\frac{0!}{0} = (0-1)![/spoiler] =>
<span class="math">-1! = \frac{1}{0}[/spoiler]

[Anonymous No.2505734]

http://www.wolframalpha.com/input/?i=0^0

http://www.google.co.uk/search?sourceid=chrome&ie=UTF-8&q=0^0

Hmm.... 0^0 is 1 or is it undefined? Wolfram Alpha and Google contradict each other.

[Anonymous No.2505780]

>>2505734
saved for history

[Anonymous No.2505828]

>>2505728
oh shi
since this, -1 equal to infinity!

[Anonymous No.2505862]

0^0 = 1 ? dear god.

[Anonymous No.2505866]

http://en.wikipedia.org/wiki/Gamma_function
also (-1/2)!=√π

[Anonymous No.2505869]

0^0 is undefined.

That's what MY teacher told me.

[Anonymous No.2505873]

0/0 = 1 ?

[Anonymous No.2505875]

0^0 is undefined

[Anonymous No.2505876]

>>2505828
it's undefined

[Anonymous No.2505924]

http://www.faqs.org/faqs/sci-math-faq/specialnumbers/0to0/

[Anonymous No.2506746]

its CONVENTION

[Anonymous No.2506761]

i thought factorial IS the gamma function only with its argument shifted by 1

[Anonymous No.2506776]

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

[poorengineer No.2506789]

this was a mindfuck for me too, but think in terms of analogy if nothing else works.

here goes:

how many different ways can three chairs be arranged? by putting them into 3x2x1=6 groups.

how many ways for 2 chairs? two groups

one chair = one group.

So if there are no chairs, there is still one group, but there just are no chairs in that one group. some faggots won't see this, but it's a counting technique that i thought of. deal with it.

[Anonymous No.2506794]

>>2505734
>implying google is a mathematical calculator on par with wolfram alpha

Anyway, factorial is just a manufactured shortcut function. By definition of said function, 0! = 1. It was made for use in certain applications where it makes sense to have 0! = 1. Such as:

>It makes many identities in combinatorics valid for all applicable sizes. The number of ways to choose 0 elements from the empty set is . More generally, the number of ways to choose (all) n elements among a set of n is .

[Anonymous No.2506799]

0! = 1 because mathematicians say so (no really).
It could objectively be 1 or 0, but when it's one, it makes stating certain formulas a lot easier (the formula for binomial coefficients comes to mind).

[Anonymous No.2506827]

>>2505627

0^0 = 1 is also by convention. Here's a good explanation.

http://www.askamathematician.com/?p=4524

[Anonymous No.2506890]

>>2506789
Zero chairs can be split into infinitely many groups, I can have 100 groups with nothing, 4.2376 groups of chair each with zero chairs, etc.

[poorengineer No.2507013]

>>2506890
i suppose you're right.

but the focus mustn't be given on the groups, but on i suppose what is the least number of "sets" which represent the total quantity, with varying magnitudes so to speak. (not talking about real sets)

in an empty classroom you have to arrange 3 chairs: first you have three possibilities, for each you have two further possibilities each, for which you have one each. what i tried to visualize was the existence of a null set of chairs (no chairs) that exists in the classroom, which equates to a "1". There are infinitely many "0 chairs" in that null set. If you give a null set a value of 0, every counting will give 0. it's a weird way to look at it, i agree. could be my way of dealing with the fact that it might have no physical significance.

[poorengineer No.2507026]

>>2507013
given there only are three chairs in the room