Why is 0! = 1?

This question is probably very baffling to several students. Many students will exclaim $0!=0$ to me, but this is incorrect. To understand why $0!=1$ , we need to first look at what $n!$ means; $n!$ is the number of ways to arrange $n$ objects in a row. And we all know that $n!=1 \times 2 \times 3 \ ... \times n$ . So shouldn’t $0!=0$ ?

Think about this, the number of ways to arrange 1 object is 1, that is, put the object there by itself. However, the number of ways to arrange $0$ object is one! Cos there is nothing to arrange so we still have one way to do it.

Give it some thought and feel free to discuss with me!

Related video by Dr James Grime

[youtube=https://www.youtube.com/watch?v=Mfk_L4Nx2ZI]

Factorial Number Theory Opinion Probability

About

KS has been teaching H2/H1 Mathematics and IB mathematics for the more than 10 years. Having taught students from all various Junior Colleges, KS adapts to students' abilities and help them better understand the topics. As someone who loves to teach mathematics and sees it as a truly useful tool in life, KS seeks to enable students to appreciate math. Therefore, his tuition mission is to motivate and cultivate students to be independent and confident thinkers.

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