Question

proof that factorial of 0 is 1

Answer 1

for the equation to be true, we must force the value of zero factorial to equal 1 and no other.
other wise 1!≠1 which is a contradiction.so yes,
0! = 1  is totally correct because as mathematicians are agreed to define and explain it that way (nothing more and nothing less) in order to be consistent with the rest of mathematics.
solving steps
to prove that 0!=1 we can simply plug 1 into the formula
n!=n×(n-1)!
1!=1×(1-1)!
1!=0!
0!=1!
hence solved

Answer 2

Answer:

Step-by-step explanation

1!= 1

2!= 1x2

3!= 1x2x3 and so on..

But notice how 3!= 2!x3

Let us look carefully, if we take n=2 in this case then (2+1)!= 2!x(2+1)

So we get a relationship here (n+1)!= n!x(n+1) correct?

Now substituting n as 0, we get

1!=0!x1

Therefore, 0!=1!=1