A book where I talk about math knowledge/fact/etc that I find interesting.
If you guys also have some interesting math facts, feel free to let me know! I might as well put them in this book.
[This book is best read with white background, sorry dark...
Ahhh, factorials. The thing you learned when you were about to start studying permutations. But, have you ever wondered, why is it 0 factorial has to equal to 1, exactly? I mean 0 isn't even a natural number!
For those who don't know what factorial is, here's the general formula.
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where n is a natural number
And here are some examples. 5! = 5 × 4 × 3 × 2 × 1 4! = 4 × 3 × 2 × 1 3! = 3 × 2 × 1
And now, I'm gonna show you why 0! = 1, mathematically and philosophically.
Mathematically 4! and 3! can actually be rewritten like this :
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Which means that our factorial formula can be rewritten as :
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Using our new formula, we can now solve what does 0 factorial equal to!
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We can now conclude that 0! = 1
Philosophically Factorials is very closely related to permutations and combinations. n! is defined to be the number of way you can arrange n objects.
For example: 3! = 3 × 2 × 1 = 6 ways, which are {(a,b,c),(a,c,b),(b,a,c),(b,c,a),(c,a,b),(c,b,a)} 2! = 2 × 1 = 4 ways, which are {(a,b),(b,a)} 1! = 1 way, which is {(a)}
Based on the definition and examples above, we can now say the number of way to arrange 0 object is 0! = 1 way, which is { }, a.k.a an empty set, which counts as 1 way.
