0! #shorts

0!!!!!

[J.P.Nery.N.]

Some high school teacher: "0! = 1 iS a PoStULaTe"

[tarfarian]

Another way to think - How many ways are there to arrange zero objects? One. (Saw it on Numberphile)

[diribigal]

Now I understand why 3! is 6. It follows from the pattern of 0!, 1!, and 2!. Thanks!

[wejoro]

I remember that several teachers say to the students "I can not proof you that 0!=1 because the function gamma is needed, and you must know integrate first". I think that the beautifulness of math is not in the complex fancy methods, but in the elegancy of simplify the math itself such that everybody can understand it and love it. Thanks for shareing.

[worldnotworld]

If you extend that to the negative integers they're all 1 as well.

[Megaluca]

If you define n! to be the number of bijections from a set with n elements to itself, you don't need to impose that this recursive relation holds to define 0!, it is 1 because there is precisely 1 bijection from the empty set to itself (the empty function).

[رشاداليامي]

There are other proofs for the zero factorial, but this proof is beautiful. Continue, creative🌹👍

[orenfivel]

0!=1 in python/C = "zero is not equal to one"

[suramanujan]

Okay, but you may also use a combinatorial proof.
It goes on like this:
n P n = n!/0! [Since, n P r = n!/(n-r)! ---> put r = n]
But,
n P n = n! [n P r = put r = n]
=> n! = n!/0!
=> 0! = 1
Tada! 🎉
Also, a second way will be to rearrange 0 objects among themselves.
Remember, a null sub-set is always present inside a set.
Hence,
0!=1 (1 and only way of arranging 0 objects among themselves) again.

[danielmagdalas]

Hello mister may we havw a video about exponential mapping on differential geometry pls?

[OscarMorales-wnql]

Buenas!es Una forma de recordar cuanto es 0! No es una demostración.
La forma de definir el Editorial para los nùmeros naturales está hecha en base a la idea de recurrencia.
En la escuela es algo que se tam cómo un hecho, la demostración necesita matemáticas superiores,

[divysaraswat]

Doubt - is this type of recursion method is a universal method or we can use this only for this case🤔🤔

[rikku]

is it right to write 1!=1x0! ?
n!=n x (n-1) x ... x 3 x 2 x 1, not 3 x 2 x 1 x 0. If we can go to 0 then why stop there, 0!=0x(-1)! = ? but (-1)! is not defined, like 0! is not if we define it this way. is showing 0! = 1 this way right ?

[nmmm]

This does not prove anything. May be 0! is sometimes 1, but other times 0 ;)

[Alaska-mkok]

This is a great proof and even simpler than the gamma function!

[HDitzzDH]

So we define 0! to be 1 based on pattern? Just like 3!=6, 2!=2, 1!=1, from 3! to 2! we divide by 3, from 2! to 1! we divide by 2 and then from 1! to 0! we divide by 1, thus 0! is 1.

[CooZaPech]

Let's follow that!
1! = 1 * 0! = 1 => 0! = 1
0! = 0 * (-1)! => 0! = 0
**seems illegal**

[Nero-Norell]

1 = 0! = 0 x (-1)! - - > (-1)! = 1/0 confirmed

[Kdd]

This proof is very nice! Never seen before

[SimsHacks]

Factorial def:
0!=1
n!=n*(n-1)! for n>=1