All of us know 0! = 1 by calculator or general knowledge, but do you know why is it so? What is the proof of the equation to be correct? Well, there is 3 proving method behind this mystery.
1. Mathematically Proving 0! = 1
Firstly, we know that factorial series of n is
From here we know by going down factorial series, it can also be expressed as
2. Graph Extrapolation Proving 0! = 1
3. Logically Proving 0! = 1
Factorial is used to show the number of possible arrangement pattern of a situation,
3! means 3 object arranged randomly, thus we can get 6 possible arrangement
Hence by logical thinking, if 1!, we only have 1 object, which we will only have 1 possible arrangement, thus the result is 1
For the same situation, if 0!, which we have 0 objects to be arranged. Thus, we will have only 1 option to arrange the object, which is just arranging the nothing in the space.
Hence by the proof of all these 3 methods, I believe you now understand why 0! = 1, which confused you so much in your school. You can now brag it in front of your friends the wisdom of 0!
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