I have been recently studying binomial theorem and in that we very frequently encounter factorials. But one queer thing which I found is $0!$. Even more queer is its value which is      $0! = 1$.   I was told this fact and I accepted it(without any proof). But I am still confused about it.  How can we prove that $0!= 1 $?
How can I prove  from first principles that $0!$ is equal to $1$?
In particular, when $x=y=z$ isn't the above expression equal to 1 and not -1?