Question

Why the value of 0! = 1.. ?? ಠಿ_ಠ​

Answer 1

Answer:

0! = 1 is correct because mathematicians agreed to define it that way (nothing more and nothing less) in order to be consistent with the rest of mathematics.

prove :

Let n be a whole number, where n!n! is defined as the product of factors including n itself and everything below it. What it means is that you first start writing the whole number n then count down until you reach the whole number 11.

The general formula of factorial can be written in fully expanded form as

n! = n·(n-1)·(n-2)·...·3·2·1

or in partially expanded form as

n! = n · (n-1)!

We know with absolute certainty that 1!=1, where n=1. If we substitute that value of n into the second formula which is the partially expanded form of n!, we obtain the following:

1! = 1 · 0!

For the equation to be true, we must force the value of zero factorial to equal 1, and no other. Otherwise, 1!≠1 which is a contradiction.

So yes, 0! = 1 is correct because mathematicians agreed to define it that way (nothing more and nothing less) in order to be consistent with the rest of mathematics.

Answer 2

Answer:

The definition of a number's absolute value is its distance from 0 . Since 0 is zero units away from itself, the absolute value of 0 is just 0 ...

and 1 is undefined..

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