I can understand why many of us have a hard time agree the fact that the value of zero factorial is equal to one. It comes throughout as one absurd statement the there’s no means it have the right to be true. We have actually a common perception the zero for being notorious since there’s something about it that can make any number connected with it either vanish or misbehave.

For instance, a big number such as 1,000 multiplied by zero becomes zero. It disappears! top top the other hand, a pretty number such as 5 separated by zero i do not care undefined. That misbehaves. So the is it s okay to be unconvinced why zero “suddenly” becomes one, a pretty number, after dealing with it v some special operation.

You are watching: Why 0 factorial is equal to 1

There space other methods to display why the explain is true. Because that this one, us will use the meaning of factorial itself. To it is in honest, through this an approach the justification is straightforward and requires tiny math.

Simple “Proof” Why Zero Factorial is equal to One


Let n it is in a whole number, wherein n! is characterized as the product the all whole numbers much less than n and also including n itself.

What it method is that you first start writing the whole number n then counting down till you with the whole number 1.

The basic formula that factorial deserve to be written in fully expanded kind as


*

*

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


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For the equation to be true, us must force the value of zero factorial to equal 1, and also no other. Otherwise, 1!≠1 i beg your pardon is a contradiction.

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

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