why factorial does not exist for negative numbers?

Answer 1

factorials exist for ALL numbers, except negative INTEGERS. this means that factorials for non-integral negative numbers exist. It also exists for all types of real numbers, even imaginary and complex numbers. This extension of the factorial function is called the gamma function. it is a smooth surface that lies on the real-imaginary coordinate space.

i have read about this in wikipedia some time last year. fortunately i still remember it.
^_^

Answer 2

Factorial is simply a notation for the product of a number and all the positive integers less than that number. It fails to exist for negative numbers basically because that contradicts the definition. There's no deep mathematical reason except perhaps that factorials are often used for counting questions where negatives don't make sense.

Answer 3

Read the post above me regarding the gamma function. Good luck with understanding it though. The first time I saw the gamma function was in differential equations class.

Just like how it says in the link, Gamma gives you a relationship for the word "factorial" with rational, irrational, and even complex numbers. But notice that this partially answers your question. If you look at the graph, you can find the factorial of a negative number as long as it is not a negative integer.

One of the exact values of the gamma function we know is gamma(1/2)=sqrt(pi).

Since gamma(x)=(x-1)!
We have that (-1/2)!=gamma(1/2)=sqrt(pi). I don't know where it would really help you but here it is.

Answer 4

Good news! It does exist for negative numbers.

The factorial function on the positive integers can be extended to not only to negative numbers but also to rational numbers, including fractions like 3/2. This extension is known at the gamma function.

Answer 5

I am an engineer,not a mathematician, so I may be all wet on this .. but..
I would say that since the multiplication of an odd number of negative terms gives you a negative answer, while an even number of terms gives a positive answer makes the progression two headed and probably renders it useless.

Answer 6

Why do you need it?

If you know what negative numbers mean, it's TOTALLY irrelevant to define a factorial for negative numbers.

Answer 7

It exists, you can define it as you wish, it just does not help much. Factorials are related to counting problems mostly.

Answer 8

Certain things in Math have the "by definition" answer and this is one of those cases.

Answer 9

n!=n*n-1*n-2*.................................*3*2*1.
(i think u know this)
if n is -ve,
for ur understanding substitute n= -1.
we get
(-1)!=(-1)*(-2)*(-3)*........................
and it will nevr end with 1 & also it will never end & and product will be infinity for all n = -ve