# Why 0!=1

1. Jul 6, 2013

### iScience

the explanation i got for this is because..

(x+1)!=(x+1)x!

and that when x=0

(0+1)!=(0+1)0!

simplified 1=0!

but this implies (0+1)!=1... i don't see how....... if (0+1)0!=0!, then for (0+1)!=1, where did the factorial symbol go? why does the factorial disappear for this? (0+1)!=(0+1)(0)(0-1)(0-2)etc... so someone please explain to me why (0+1)!=1

2. Jul 6, 2013

### micromass

Staff Emeritus
We have that $0+1=1$, thus $(0+1)! = 1! = 1$.

3. Jul 6, 2013

### Simon Bridge

The factorial sumbol vanished on the RHS because the factorial was evaluated.

(0+1)0! = (0+1)!
=> 1x0! = 1!
=> 0! = 1

4. Jul 6, 2013

5. Jul 7, 2013

### symbolipoint

That video is perfect. That is the best explanation I ever saw. The guy simply followed the pattern.