Factorial of 0 Proof:
since we know that
n!=n(n-1)(n-2)(n-3)…….(n-n+2)(n-n+1)(-n-n)
where n belongs to positive integer
Examples.
2!=2(2-1)=2(1)=23!=3(3-1)(3-2)=3.2.1=6Now we will prove that 0!=1 is equal to one.
As
n!=n(n-1)(n-2)(n-3)!
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)…….3.2.1for 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)!=-\inftyHence 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^1dividing x on both sides.
\frac xx=x^0.\frac xx1=x^0.1\boxed{1=x^0}hence any number power zero is equal to 1