factorial function??? algebra 2?

Question

what does 0! = 1 mean?
i read it... if 0! = 1 why cant 0! just be x or y?

Answer 1

By definition n! = 1*2*3*...*(n-1)*n for n = 1, 2, 3, etc.
According that definition (n-1)! = 1*2*3*...*(n-1) for n = 2, 3, etc.and we have:
n! = n*((n-1)!) - that's true for each integer n = 2, 3, 4, etc.
How to define 0! then? Let us require the above to be true not only for n = 2, 3, 4, etc., but also for n = 1, we'll have
1! = 1*0!
But, having 1! = 1 the above will be true if we define 0! = 1 only! So there is a good reason for that seemingly unnatural definition - some properties to remain valid being extended.
The situation is quite similar to the better known a^0 = 1 if a is not 0: you know that a^x/a^y = a^(x - y) and if x = y it remains true if a^0 = 1.

Answer 2

As the others said 0! = 1 is true by definition. What do you mean 0! could just be x or y? x and y do not of themselves denote anything. Naming a number x is just a meta-language to refer to any arbitrary or unknown number.

0! must be equal to 1 because factorials have many applications in combinatorial formulas. For example, the number of ways of arranging 3 distinct books on a shelf is 3! = 6. If you had 0 books, there would be only one way. As another example, suppose you want to count the number of distinct k element subsets of a set containing n elements. The formula for doing this is n!/[k!(n-k)!]. For instance, the number of distinct 2 element subsets of {1, 2, 3} is 3!/(2!1!) = 3. Clearly the set {1, 2, 3} has only 1 subset with 0 elements (the empty set). Hence, we would like 3!/[0!3!] = 1 so again, it is useful to define 0! = 1

Answer 3

The factorial operator has this property: (n + 1)! = (n + 1)*n! for n >= 1. We would like that relation to hold also for n = 0, so we want (0 + 1)! = (0 + 1)*0!. This demands that 0! = 1.

Answer 4

Its basically a definition. 0! = 1. It is defined as such to ensure properties of mathematics don't fail at 0!.

Actually, x or y could = 0! (but that in turn just equals 1).

(NOTE: "!" for example, 3! = 3*2*1 = 6.)

Answer 5

It's just a notation.

It means 0 * ! = 1

So you have to find a value of ! so that when you multiple it by 0 it = 1.