2006-08-10 19:20:55 · 11 answers · asked by shafi 2 in Science & Mathematics ➔ Mathematics
Usually n factorial is defined in the following way:
n! = 1*2*3*...*n
But this definition does not give a value for 0 factorial, so a natural question is: what is the value here of 0! ?
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.
How can we fit 0! = 1 into a definition for n! ? Let's rewrite the usual definition with recurrence:
1! = 1
n! = n*(n-1)! for n > 1
Now it is simple to change the definition to include 0! :
0! = 1
n! = n*(n-1)! for n > 0
2006-08-10 20:12:29 · answer #1 · answered by awesomeash 2 · 0⤊ 0⤋
It depends on what we're allowed to use. Ordinarily, I'd just accept that 0 isn't 1.
Let's say you're willing to admit that not all numbers are equal. Under that assumption, I can prove that 0 isn't 1:
Take x and y such that x != y. Subtract y from each side. Now you have x-y != 0. Since we assumed that x and y aren't equal, then x-y isn't 0. Thus we can divide each side by x-y, giving the desired 1 != 0.
2006-08-11 02:34:27 · answer #2 · answered by Charles G 4 · 0⤊ 0⤋
3! = 3*2*1*0! , 2! = 2*1*0! , 1! = 1*1*0! , 3!/3!=1 x!/0!=x!/1 well i forgot it cuz about 3years that i didn't play maths but i'll be back! just in time
2006-08-11 02:47:23 · answer #3 · answered by karim b 1 · 0⤊ 0⤋
another way of describing a factorial is the no of ways of arranging n different objects in n places for ex the no of ways of arranding ab in 2 places is 2! =2 since we can arrange 0 things in 0 places in one way 0! is one
2006-08-11 05:27:20 · answer #4 · answered by keerthan 2 · 0⤊ 0⤋
Try plugging 0 into the gamma function which is expanded factorial system.
2006-08-11 03:05:01 · answer #5 · answered by anonomous 3 · 0⤊ 0⤋
hmm, calculator said 0!=1
2006-08-11 02:42:51 · answer #6 · answered by NR 2 · 0⤊ 0⤋
It is simply a trick which only works if a person allows division by zero. And seeing how as division of zero is not allowed, there can be no "proof".
2006-08-11 02:26:49 · answer #7 · answered by old dirty bastahd 2 · 0⤊ 0⤋
0! is defined as 1, so is -1!, -2! and so on.
There is no proof....its just defined as so.
2006-08-11 02:28:28 · answer #8 · answered by ali 6 · 0⤊ 0⤋
0! = O x - 0 x - 01 and so forth.
calculate and u get tha answer .
(:
2006-08-11 02:27:06 · answer #9 · answered by Wide Ruled Paper 3 · 0⤊ 0⤋
http://en.wikipedia.org/wiki/Factorial
2006-08-11 04:04:41 · answer #10 · answered by Polymath 5 · 0⤊ 0⤋