Factorial of 0 - a convenience? If I am correct in stating that a factorial of a number ( of entities ) is the number of ways in which those entities can be arranged, then my question is as simple as asking - how do you conceive the idea of arranging nothing ? 
Its easy to conceive of a null element in the context of arrays, for example - so you say that there is only one way to present a null element. 
But, in layman terms - if there are three humans $h1, h2, h3$ that need to be arranged to sit on three chairs $c1, c2, c3$ - then how do you conceive of a) a null human, and b) to arrange those ( that ? ) null humans ( human ? ) on the three chairs ? 
Please note that referral to humans is just for easy explanation - not trying to be pseudo-philosophical. Three balls to be arranged on three corners of a triangle works just fine. So basically, how do you conceive of an object that doesn't exist, and then conceive of arranging that object ?
So, in essence ... is $0! = 1$, a convenience for mathematicians ? Not that its the only convenience, but just asking. Of course, there are many. 
If yes, then its a pity that I can't find it stated like so anywhere. 
If not, then can anybody suggest resources to read actual, good proofs ? 

There is exactly one way to arrange nothing: the null arrangement. You've misused your chair analogy: when you arrange null humans, you do it on null chairs, and there is exactly one way to do this. 
Perhaps the following alternate definition will make things clearer. Suppose I have $n$ cards labeled $1, 2, ... n$ in order, and I shuffle them. Then $\frac{1}{n!}$ is the probability that they will stay in the original order. If $n = 0$, this probability is $1$ since $0$ cards can only be arranged in one possible order. 
