Can anyone prove that 0!=1? Thanks!?

0! is actually defined to be equal to 1 to keep the factorial consistent with its property of recursion. Notice that for any positive integer n, n! = n(n-1)!. Clearly, 1! = 1, so using this property, we have

1 = 1! = 1(1-1)! = 1(0)! = 0!

0!=1 simply by definition. The factorial function is defined recursively by 0!=1, n!=n*(n-1)! for all natural numbers n>0. I hope that helps!

No, it cannot be proven because 0! = 1 is a defined quantity like any number to the 0th power is defined to be 1.

I can explain to you why 0!=1.

Think of 1! as how many different ways you can arrange 1 card. it's 1 way. 2! is how many ways you can arrange 2 cards, which is 2 different ways. 3! is 3 cards, so 6 ways, and so on. But if you have no cards, you can only arrange them in 1 way. I hope that makes sense for you :)

easy

how many numbers are showing below?

0

that's imposible.

At least from what i know about factorials.

0!=0