Question

how can 0!=1! ? doesn't it defy the fundamentals of mathematics?

Answer 1

It's a definition. Everything else works if we define it to be so. :)

Answer 2

Also, there is only one way to re-arrange a set of zero objects.

Answer 3

First of all n! is define as the product of the first n natural numbers.
Since 0 is not a natural number, we can't use that definition. Then it is up to use to give a meaning to 0!. Then if we define 0!=1 everything works nicely.

Answer 4

Here is another nice answer: http://mathforum.org/library/drmath/view/57128.html

Answer 5

that was quite enlightening! thank you both