Zero Factorial - Numberphile
Why Mathematics Stack Exchange recommends it
Mathematics Stack Exchange answerers point people to it when someone asks why 0! = 1, since it gives the simple recurrence argument in an accessible way.
Recommended by 3 people across 3 different months, 2014 to 2020.
What it is
A short Numberphile video in which Dr James Grime explains why 0! equals 1. He argues from the factorial recurrence, noting that n! = (n+1)!/(n+1) only works at n=0 if 0! is 1, and also touches on the empty arrangement and the gamma integral.
What people said
Recommends Stefan4024 · 2014-01 · Mathematics Stack Exchange · on “Proof of $0! = 1$”
Note that: $$n! = \frac{(n+1)!}{n+1}$$ So you can apply this for $0$. Actually it's quite nicely explained here [this video]
Recommends user1337 · 2014-06 · Mathematics Stack Exchange · on “Factorial of zero is 1. Why?”
See this video [this video] . Two reasons are: We want the functional equation $n!=(n-1)!n$ to hold when $n=1$. $0!$ should be the number of different ways of arranging $0$ items in a row. There is precisely one way of doing it (the empty arrangement).
Recommends Thomas · 2015-07 · Mathematics Stack Exchange · on “Why is $0! = 1$ the same as $1! = 1$?”
You should watch this Numerphile video on Youtube: [this video] Here the argument is made that $0!$ should be one because then the rule $$ n! = \frac{(n+1)!}{n+1} $$ is true even for $n=0$. One can make other arguments, this is just one.
Cites Simon Moore · 2015-03 · Mathematics Stack Exchange · on “How can $0!=1$ if the definition of factorial is $n!=n\times (n-1)!$”
Its a pretty basic question. If the definition of factorial is $n!= n\times(n-1)!$, then how can $0!=1$ since if we feed $0$ into the equation we get $0!=0\times (-1)!$? This comes after a Numberphile video [this video] where they explained that you can write $4!=\frac{5!}5$ then you can say that $0!=\frac{1!}1$ which equals $1$. They also say that there is one way to arrange nothing but I would say there are $0$ ways to arrange nothing since there is nothing to arrange.
Cites Sander Schaeffer · 2020-10 · Mathematics Stack Exchange · on “Why does the order of variables in an equation matter compared to reduction or addition?”
Some things in live are just obvious and we have to take them for granted, just like that 1+1 is (almost) always equal to 2. Yet, I sometimes wonder behind some simple mechanics, such as the following. In any addition equation, where we increase either X or Y, such as X+Y or X * Y, the order of the variables is irrelevant. Both 7+3 and 3+7 make 10. Reductions, however, the order is relevant; for such 7-3=4 and 3-7 = -4 Many explanatory videos, such as Zero is still One (Factorial) [this video] and Russel's Paradox [LINK] , often fascinate me and I was hoping for some thoughts about the above. Is it something we, indeed, have to take for granted or has some smart mind ever thought why this is, the