# I'll give you 10$ of my mylot earnings if .......

By krishna183

@krishna183 (2286)

India

October 7, 2006 7:10am CST

If you can prove 0! = 1 ... thats is ( 0 factorial = 1 .. how ?? ) ... for the brainy ones out here haha

4 responses

@bblessed (1822)

• United States

7 Oct 06

A first way to see that 0! = 1 is by working backward. We know that:
1! = 1
2! = 1!*2
2! = 2
3! = 2!*3
3! = 6
4! = 3!*4
4! = 24
We can turn this around:
4! = 24
3! = 4!/4
3! = 6
2! = 3!/3
2! = 2
1! = 2!/2
1! = 1
0! = 1!/1
0! = 1
In this way a reasonable value for 0! can be found.

1 person likes this

@krishna183 (2286)

• India

8 Oct 06

great .. u are very smart !! .. u gave me exactly the answer i was expecting .. there isnt any other way of proving it .. anyways i was kidding about the 10$ haha .. :-) .. dont mind .. bye

@crowdofgirls (557)

• United States

8 Oct 06

well didn't this thread turn out with a fun twist ending.

@register (1065)

• India

2 Dec 07

That is not the exact answer..
Mathematicians defined 0! to be 1. it cannot be proved actually..
0!=1 needed to be set to make the rest of the peripheral stuff work..Like for eg : x^0 = 1 in order to make the laws of exponents work even when the exponents cannot be thought of as repeated multiplication.

@kundalini444 (195)

• Italy

31 Dec 07

This is the real exact answer. I may be not good at english since I'm not a native speaker, but I'm Ph.D. in Mathematics, so... the actual definition of factorial is:
0!= 1 (is DEFINED to be)
n!= n x(n-1)!(recursively defined by induction for any n 0)
If you put it that way, you can observe that all operations and rules for factorials on positive integers are consistent with the definition of 0! = 1.
The same is true with the definition of x^0 = 1 because that makes 0 consistent with the rules of division between powers
1 = x^n / x^n = x^(n-n) = x^0