Question

by logic, 4!= x3x2x1, 3!=3x2x1, why 1!=1 and 0!=1

Answer 1

I think '0!=1' is by convention.

Answer 2

yeh it's just one of the special rules

Answer 3

a logical explanation please, why mathematicians decided this way

Answer 4

they are humans, no gods, so I think there's a reason behind this

Answer 5

would you accept the explanation
n!= n*(n-1)!
so if n=1
1!= 1*0!
therefore 1=0!

Answer 6

what about 0!=1

Answer 7

its only where n is greater than or equal to 1
0!=1 is more like an assumption and there's really no actual way to prove it

Answer 8

\[n!=n*(n-1)!\\\Rightarrow (n-1)!=\frac{n!}{n}\\\\\text{Substituting n=1,}\\\\(1-1)!=\frac{1!}{1}\\\\\Rightarrow 0!=1\]

Answer 9

what about (-2)!

Answer 10

there is no (-2)!

Answer 11

if there is 0!, there is no reason theres no (-2)!

Answer 12

just read the first three lines of: http://en.wikipedia.org/wiki/Factorial

Answer 13

but theres no line saying negative numbers or non-integer(like 3.514) numbers CAN NOT have factorial..

Answer 14

the very first line says "In mathematics, the factorial of a non-negative integer n, ......"

Answer 15

what about the factorial of a negative number, or a decimal number.. what would they be

Answer 16

for those who did some programming, I made a program using while loops that gives me the factorial of whatever number...

Answer 17

and astonishingly..

Answer 18

(please reply if u have any programming experience with loops...)

Answer 19

astonishingly would give you a complex infinity error if your input for n is a negative number

Answer 20

nop..

Answer 21

far from that...

Answer 22

when i did factorial of 1, it gave me 1... and when i did factorial of 0, it actually gave me 1 too..

Answer 23

n! is a sequence with integer values for nonnegative n

Answer 24

and factorial of any negative number gives also 1...

Answer 25

well the rule states nonnegative integer. so ZERO is included.

Answer 26

did you create a function loop that when the input for n is a negative value that the answer would yield 1?

Answer 27

not at all

Answer 28

the program is written in python, through pure logic, no exceptions are defined

Answer 29

written in python:

def factorial(n):
i=1
a=1
while i<=n:
a=a*i
i=i+1
return a

Answer 30

your while i<=n statement returns a value of 1

Answer 31

try this :

def factorial(n):
i=1
a=1
while i<=n:
a=a*i
i=i+1
return a
print "BAD INPUT !"

Answer 32

only when n is less than 1.9999999

Answer 33

@ganeshie8 your return a has bad incantation, it should be placed after the loop is completely finished

Answer 34

\[n!\neq0/;\forall n\]

Answer 35

yeah my code will not work as well :(

i think your code is not entering while loop at all for negative integers.
it is simply returning the value of a

Answer 36

apply that zero rule

Answer 37

yes ganesh. it's just going to print or display 1 when a negative value is the input

Answer 38

factorial in programming has more than 100 formulas

Answer 39

\[! == Product[k, {k, 1, n}] /; Element[n, \\mathbb{Z}s] && n >= 1\]

Answer 40

but what's truly fascinating is.. when you program through pure logic, as you can see in the program, it logically multiplies every numbers from the input, descending til 1. And when you do that, if you enter 1 as the input, it gives 1. If u enter 0 as input, normally through the logic, it would be absurd, but the program still gives 1

Answer 41

which perfectly fits the mathematical rules that are built centuries ago, when machines didn't exist yet

Answer 42

but zero is 1 secondary to empty product rule

Answer 43

also, have you looked at the list prod function in python?

Answer 44

'but zero is 1 secondary to empty product rule' what do u mean by that

Answer 45

what do you get when you raise any number (n) to zero? with the exception of n=0

Answer 46

1

Answer 47

then what is zero raised to zero?

Answer 48

if you're programming, you can set 0^0=1 when representing an empty product

Answer 49

if u program an exponential function using a pure logical algorithm, i think there is no need to add an exception, everything will just display as it actually is mathematically

Answer 50

on what logic would you set the domain and range of the function then?

Answer 51

there's no need to set them, with any input, the output will never reach 0 or below

Answer 52

There is a negative factorial but not for negative integers.

The factorial function can be extended so that it is defined for all real numbers (and complex numbers) except for negative integers. It is extended by using the gamma function. (see source).
Source(s):
http://en.wikipedia.org/wiki/Factorial

Answer 53

how would you tackle the problem of providing the factorial of multiple elements in a set?

Answer 54

ie: {2, 3, 5, 7, 11}!

Answer 55

what does this mean? I only know what factorial is

Answer 56

the factorial of {2, 3, 5, 7, 11}

Answer 57

or series expansion at infinity

Answer 58

give me an example please, I'm not sure what you mean by a factorial of multiple elements in a set

Answer 59

I just gave you one

Answer 60

{2, 3, 5, 7, 11}!

Answer 61

yes, what does {2, 3}! mean?

Answer 62

2x1x3x2x1 or what..

Answer 63

btw, I just made a simple python program using PURE LOGIC, no exceptions are added, and computer seems to behave the same way as the actual mathematics, hence, 0^0 gives one

def power(x,n):
a = 1
i = 0
while i < n:
a = a * x
i = i + 1
return a

Answer 64

nice discussion with you panlac01, have to go sleep mate, we can talk about it tomorrow ;)

Answer 65

I know this one!

\((n - 1)! = \Large {n! \over n}\)