**Factorial of 0 Proof**:

since we know that

n!=n(n-1)(n-2)(n-3)…….(n-n+2)(n-n+1)(-n-n)n!=n(n-1)(n-2)(n-3)…….3.2.1where n belongs to positive integer

**Examples.**

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

As

n!=n(n-1)(n-2)(n-3)!n!=n(n-1)!**Put **n=1

**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)……**

**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^1x^{1}=x^0.x^1**dividing x on both sides**.

**hence any number power zero is equal to 1**