Proof of Zero Factorial Equal To One | What is zero factorial |

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Proof of Zero Factorial Equal To One |
0!=1 |
To prove that zero factorial is equal to one |
#Zero factorial |
What is zero factorial |
To derive Zero Factorial Equal To One |
Lecture on zero factorial |
Result of zero factorial |
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Explain zero factorial
The factorial of a number, N, is equal to the product of all positive integers less than and equal to N.

N! = N x (N-1) x (N-2) x … x 3 x 2 x1

zero factorial
The factorial of 0 is equal to 1.

Symbolically, 0! = 1

According to the convention of empty product, the result of multiplying no factors is a nullary product. It means that the convention is equal to the multiplicative identity.
The answer of 0 factorial is 1. There are no calculations, nothing! All you have to do is write down 1 wherever and whenever you see 0!
By definition, a zero factorial is equal to one, just as 1! is equal to one because there is only a single possible arrangement of this data set.
Zero Factorial
Zero Factorial is equal to 1. Or in equation, 0! = 1.
I can understand why many of us have a hard time accepting the fact that the value of zero factorial is equal to one. It comes across as an absurd statement that there’s no way it can be true. We have a common perception of zero for being notorious because there’s something about it that can make any number associated with it either vanish or misbehave.

For instance, a large number such as 1,000 multiplied by zero becomes zero. It disappears! On the other hand, a nice number such as 5 divided by zero becomes undefined. It misbehaves. So it is okay to be skeptical why zero “suddenly” becomes one, a nice number, after treating it with some special operation.

There are other ways to show why the statement is true. For this one, we will use the definition of factorial itself. To be honest, with this method the justification is simple and requires little math.

Simple “Proof” Why Zero Factorial is Equal to One
Let nn be a whole number, where n!n! is defined as the product of all whole numbers less than nn and including nn itself.

What it means is that you first start writing the whole number nn 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 = 1n=1. If we substitute that value of nn into the second formula which is the partially expanded form of n!n!, we obtain the following:

1! = 1 · 0!