0!=1.........why????

My queation is that why 0! is equal to 1.Can you prove this?....Lr mr try..I know there will be a smile on your face because this is a very stupid way to prove this?

You know  
                      n!=n*(n-1)!
This implies                    
                      n!/(n)=(n-1)!
put n=2   then
                            
                      2!/2=1!=1     is this right? .....yes

now put n=1
                   then 1!/1=0!=1  
                 
So 0!=1 is proved. I know that it is a very stupid way but not to much bad.

Divisibility Rules...why????

Hey...here we are...we have all taught about the ways form which we can find that whether any number is divisible form 2 or 3 or some number or not.Like we can say that 13122 is divisible from 3 because we know the sum of digits,1+3+1+2+2=9,is divisible by 3.But is this number is divisible by 11?Think about it.
      I've some questions, why is this so??why this rule is not for 7?what we were not taught the rule of divisibility from 7??I've the answer.It's really simple.Let we have a no. N and it's digit are ABC.
So we can write N as

N=ABC=Ax100+Bx10+C

We can write this as..

N=abc=(Ax99+A)+(Bx9+B)+C

We know 99 &9 is divisible from 3

So Ax99+Bx9  is divisible from 3.Now here's left only.

A+B+C

If this is divisible by 3 then the no. N will be divisible by 3.That's it.Here is the rule for divisibility from 3.
We can now try this for 11

Let we have a no. N

N=ABCDEF=Ax100000+Bx10000+Cx1000+Dx100+Ex10+F

We can write it as.

F=F

Ex10=11xE-E

Dx100=Dx99+D

Cx1000=1001xC-C

Bx10000=9999xB+B

Ax100000=100001xA-A

We know 11,99,1001,9999,100001 are divisible from 11.So here is left only F-E+D-C+B-A.If this is divisible by 11 then N is divisible by 11.

We can find all these rules from this method.Let for 3 coefficient for digit is 1 1 1 1 1 ....for 11 these are 1-1 1 -1 1 -1.......We can find them for all the numberss we want.It tried to make for some...

For 3==1 1 1 1 1 1 1 1....
      11==1 -1 1 -1 1 -1...
       7==2 -1 -3 -2 1 3 2 -1 -3 -2 1 3.......
       9==1 1 1 1 1 1....
     13==-4 -1 3 4 1 -3 -4 -1 3.......
So this is the basic method for finding the  divisibility rule for the numbers and we got the answer why we were not taught the rule of divisibilityfrom 7.Try to do some more........