Yahoo Answers: Answers and Comments for What is the value of 0!? [Mathematics]
Copyright © Yahoo! Inc. All rights reserved.
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
From rumple
enSG
Fri, 13 Sep 2019 18:06:29 +0000
3
Yahoo Answers: Answers and Comments for What is the value of 0!? [Mathematics]
292
38
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
https://s.yimg.com/zz/combo?images/emaillogosg.png

From llaffer: 1
https://www.wolframalpha.com/input/?i=0%21
...
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
Fri, 13 Sep 2019 18:08:57 +0000
1
https://www.wolframalpha.com/input/?i=0%21
Another way to look at it is "how many ways can you arrange "n" objects".
If it was 3 objects, it's 6 ways.
If 2 objects, it's 2 ways.
If 1 object, it's 1 way.
If 0 objects, it's 1 way.
so 0! = 1

From billrussell42: The value of 0! is 1, according to convention....
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
Fri, 13 Sep 2019 18:08:31 +0000
The value of 0! is 1, according to convention.
see link for discussion on this.

From David: The value of 0! = 1
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
Sat, 14 Sep 2019 12:49:44 +0000
The value of 0! = 1

From Ray: The value of 0! is 1.
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
Fri, 13 Sep 2019 18:08:36 +0000
The value of 0! is 1.

From cosmo: n! = Γ( n + 1)
0! = Γ( 0 + 1) = 1
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
Mon, 16 Sep 2019 21:27:25 +0000
n! = Γ( n + 1)
0! = Γ( 0 + 1) = 1

From Krishnamurthy: 0! = 1
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
Sat, 14 Sep 2019 03:23:10 +0000
0! = 1

From JOHN: The value of 0! is wholly a matter of definiti...
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
Fri, 13 Sep 2019 21:52:26 +0000
The value of 0! is wholly a matter of definition. Once we have defined n! for the positive integers, the usual next step is to examine whether we can assign a meaning to 0! in such a way that the rules we have established for the manipulation of n! for positive integers continue to hold. We are free to define 0! to be 2 but this would not secure the goal of consistency for the whole set of nonnegative integers. It turns out that 0! = 1 (this can’t be proved because it is a choice) is just the ticket. It for instance allows us to use n!/[r!(n – r)! (1 ≤ r≤ n) for binomial coefficients. Note that we can even extend the idea of x! to any nonnegative real number x, for instance π!, but I won’t go into this.

From Dixon: It is taken as being 1 because that is the val...
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
Fri, 13 Sep 2019 18:35:46 +0000
It is taken as being 1 because that is the value we need it to be for making factorials conveniently consistent with combinatorial formulas. So without 0! = 1 we would have to abandon using factorials anyway.
There is a sort of worry that perhaps it should be 0 but then all factorials would also be zero. It all comes down to how we defined factorial in the first place. And one of the well known neat ways out of this is to define factorial recursively as
n! = n x (n  1)!
where 0! = 1
This cunningly makes the terminating value of zero the only factorial that is given an explicit value and all the other factorials are dependent on it, so it can't be wrong in itself.

From F: Zero! Why are you shouting?
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
Mon, 16 Sep 2019 23:50:57 +0000
Zero! Why are you shouting?

From Raymond: 5! = 1*2*3*4*5
therefore
4! = 5! / 5 = 1*2*3*4...
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
Mon, 16 Sep 2019 21:31:35 +0000
5! = 1*2*3*4*5
therefore
4! = 5! / 5 = 1*2*3*4 (the 5 cancels out)
therefore
3! = 4!/4
2! = 3!/3
1! = 2! / 2 = 1
therefore
0! = 1! / 1 = 1/1 = 1
It is the only way to make 0! consistent in the factorial operation.

From Jim: We ind factorials mostly in combinations and p...
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
Mon, 16 Sep 2019 18:29:07 +0000
We ind factorials mostly in combinations and permutations.
To be consistent, we have defined 0! To be 1

From Engr. Ronald: 0! = 1 answer//
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
Mon, 16 Sep 2019 09:58:13 +0000
0! = 1 answer//

From Anonymous: The value is 1, 0, 1, 0, 1
0 1.
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
Sun, 15 Sep 2019 20:16:41 +0000
The value is 1, 0, 1, 0, 1
0 1.

From Philomel: 0!=1...............
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
Sun, 15 Sep 2019 03:24:09 +0000
0!=1...............

From Anonymous: 0! = 1 .
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
Sun, 15 Sep 2019 02:06:28 +0000
0! = 1 .

From sepia: 0! = 1
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
Sat, 14 Sep 2019 12:01:50 +0000
0! = 1

From Andrea: The value of 0 would be 1
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
Sat, 14 Sep 2019 05:33:00 +0000
The value of 0 would be 1

From ?: By definition, 0! = 1
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
Fri, 13 Sep 2019 20:32:55 +0000
By definition, 0! = 1

From God: 1 .
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
Fri, 13 Sep 2019 18:08:51 +0000
1 .

From Emily: The value of 0 is equal to 0 or 1
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
Sun, 15 Sep 2019 08:59:48 +0000
The value of 0 is equal to 0 or 1

From bradley H: The value of 0 is zero but it's also 1.
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
Sun, 15 Sep 2019 00:22:32 +0000
The value of 0 is zero but it's also 1.

From Paul: 0 value is 0 or 1 or 100% or 0% or infinity
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
Sat, 14 Sep 2019 06:53:47 +0000
0 value is 0 or 1 or 100% or 0% or infinity

From Daniel: That's the middle of the whole graphing pl...
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
Fri, 13 Sep 2019 22:55:17 +0000
That's the middle of the whole graphing plane in x and y coordinate.

From Anonymous: The value of 0! is ****ZERO**** </shouting>
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
Sat, 14 Sep 2019 04:05:05 +0000
The value of 0! is ****ZERO**** </shouting>

From Lôn: Zero....................
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
https://sg.answers.yahoo.com/question/index?qid=20190913180629AAZYrmg
Fri, 13 Sep 2019 18:30:24 +0000
Zero....................