What is 0 to the power 0?

I can underst& why many of us have a hard time accepting the fact that the value of zero factorial is equal lớn one. It comes across as an absurd statement that there’s no way it can be true. We have sầu 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 lớn be skeptical why zero “suddenly” becomes one, a nice number, after treating it with some special operation.

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There are other ways lớn 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 lớn One


Let n be a whole number, where n! is defined as the sản phẩm of all whole numbers less than n & including n itself.

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What it means is that you first start writing the whole number n then count down until you reach the whole number 1.

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


*

*

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


*

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

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

You might also be interested in:

Factorial Notation, Formula, & Basic ExamplesDividing FactorialsSimplifying Factorials with Variables


MATH SUBJECTSIntroductory AlgebraIntermediate AlgebraAdvanced AlgebraAlgebra Word ProblemsGeometryIntro lớn Number TheoryBasic Math Proofs
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