if 0!=1! then what is the actual value of 0 & 1

Question

We know 0!=1 & 1!=1 .

So 0!=1!, Here its seen that The value of 0 & 1 is Same. But this is Wrong. There must be difference between the Value of 0 & 1.

There what value do they signify?

Answer 1

0! = 1 is the result of the definition of factorial.

n! = 1 · 2 · 3 · 4 · ... · n

And that can be written

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

Or

n! = n(n - 1)!

Therefore

0! = 0(0 - 1)

0! = 0

 

This result is similar to the necessary conclusion that x⁰ = 1, in that it is based on prior definitions.

Answer 2

Actually, you cannot conclude that if 0! = 1!, then 0 = 1.  The fact that f(a) = f(b) is not sufficient to conclude that a = b.  For example, sin(π) = sin(5π) = 0, but that does not lead to the conclusion that π = 5π.

 

0! is defined as equal to 1.