Factorial of 0, Proof and Examples

Leave a Comment / Mathematics / By Azhar

Factorial of 0 Proof:

since we know that

$n!=n(n-1)(n-2)(n-3)…….(n-n+2)(n-n+1)(-n-n)$

Factorial of 0

$n!=n(n-1)(n-2)(n-3)…….3.2.1$

where n belongs to positive integer

Examples.

$2!=2(2-1)=2(1)=2$

$3!=3(3-1)(3-2)=3.2.1=6$

Now we will prove that 0!=1 is equal to one.

As

$n!=n(n-1)(n-2)(n-3)!$

Factorial of 0

$n!=n(n-1)!$

Put $n=1$

$1!=1(1-1)!$

$1!=1(0)!$

$1!=(0)!$

$\boxed {1=0!}$

Hence factorial of 0 is equal to 1

Why it is not possible to have a negative factorial ?

Is factorial define for nagative numbers?

why can not have a negative factorial?

why no negative factorial?

$n!=n(n-1)(n-2)(n-3)…….3.2.1$

for negative integers

put $n=-m\in Z$

$(-m)!=-m(-m-1)(-m-2)(-m-3)…….(-m-m)(-m-m-1).........$

$(-m)!=$ (negative).(negative).(negative).(negative)…………(negative).(negative)……

$(-m)!=-\infty$

Hence prove that negative factorial does not exist.

Power zero is equal to ?

power zero is equal to 1

what does zero power mean

Anything power zero is equal to

$x^{n+1}=x^n.x^1.....(a)$

put $n=0$ in eq(a)

$x^{0+1}=x^0.x^1$

$x^{1}=x^0.x^1$

dividing $x$ on both sides.

$\frac xx=x^0.\frac xx$

$1=x^0.1$

$\boxed{1=x^0}$

hence any number power zero is equal to 1

Leave a Comment Cancel Reply