Question

Is there any way to prove that 0!=1
?

Answer 1

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Originally Answered: How can I prove 0! = 1?

The factorial of a number is defined as:

n!=n∗(n−1)∗(n−2)∗(n−3)∗...∗1n!=n∗(n−1)∗(n−2)∗(n−3)∗...∗1

So:

5!=5∗4∗3∗2∗1=1205!=5∗4∗3∗2∗1=120

4!=4∗3∗2∗1=244!=4∗3∗2∗1=24

Hence, it can be observed that :

n!=n∗(n−1)!n!=n∗(n−1)!

From this equation, substituting 1 for n:

1!=1∗(1−1)!1!=1∗(1−1)!

1!=1∗0!1!=1∗0!

0!=1/10!=1/1

0!=1

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