Why does 0!=1 Why does i happen?

[csp4.0 1]

Why does 0!=1 (zero factorial equals one). I've been confused by this for a long time. So why does it happen? If you were looking for an answer then you'd be at the wrong place, actually I'm asking for an answer. What is factorial?Well factorial is when a number is multiplied by all the numbers below it (except for zero) so 3! (three factorial '!' being the symbol for factorial) equals 6 because 3x2x1=6, 4!=24 because 4x3x2x1=24. The question is simple why does 0!=1?

Edited December 3, 2007 by csp4.0 (see edit history)

[anwiii 17]

Why does 0!=1 (zero factorial equals one). I've been confused by this for a long time. So why does it happen? If you were looking for an answer then you'd be at the wrong place, actually I'm asking for an answer. What is factorial?
Well factorial is when a number is multiplied by all the numbers below it (except for zero) so 3! (three factorial '!' being the symbol for factorial) equals 6 because 3x2x1=6, 4!=24 because 4x3x2x1=24. The question is simple why does 0!=1?

man...is this a homework assignment or somethin'? the answer can be found here.... http://mathforum.org/dr.math/faq/faq.0factorial.html

from your example, it explains to work backwards, not forwards so when working backwords, you have to divide, not multiply.

you already defined 4!=24 , 3!=6 , 2! = 2 and 1! = 1

going backwards, you will see that 3!=4!(24 remember)/4 =6 , 2!=3!(6 remember)/3=2 , 1!=2!/2=1

so what do you think 0! is now? well, 0! would equal 1!/1. since 1!=1, 1/1 is 1 and that is what 0! equals. ONE!

[crazyfray 0]

Why does 0!=1 (zero factorial equals one). I've been confused by this for a long time. So why does it happen? If you were looking for an answer then you'd be at the wrong place, actually I'm asking for an answer. What is factorial?
Well factorial is when a number is multiplied by all the numbers below it (except for zero) so 3! (three factorial '!' being the symbol for factorial) equals 6 because 3x2x1=6, 4!=24 because 4x3x2x1=24. The question is simple why does 0!=1?

Lol...you confused me greatly there. I thought you meant in programming terms, since ! is used to mean not...so while x=x (x is equal to itself), x!=y (x is not equal to y).

Which is why I thought 'what an idiot, asking why 0 isn't equal to 1'. More fool me!

if post-title.content.firstglance != obvious-to-stupid-crazyfray then
irrelevant-pseudocode.add
end if

[omarsdali 0]

I thought you meant in programming terms, since ! is used to mean not...so while x=x (x is equal to itself), x!=y (x is not equal to y).

I thought the same thing at first too.

[demonatashadow 0]

because there cannot be a 0duuuuuhhhhh

[Liam_CF 0]

Not a clue why, but you've now taught me what the ! (factorial) is! I've always wanted to know what that button on my calculator meant.

[Archangel_Baw 0]

I have NO idea but when you figure it out, please post the answer so I don't go insane with you!

[bertman 0]

why is 0!=1the answer is as follows:sincen!=n(n-1)!then5! = 5(5-1)! = 5(4)!4! = 4(4-1)! = 5(3)!3! = 3(3-1)! = 3(2)!2! = 2(2-1)! = 2(1)!1! = 1(1-1)! = 1(0)!since 1(0!) = 1 then 0! = 1hope I was able to help.

Edited December 5, 2007 by bertman (see edit history)

[shadowx 0]

I guess the answer is just because maths doesnt seem to like Zeros, for example, zero multiplied by zero equals one... but how...If you look at it like this:

1 X 2 is the same as saying i have one bucket of two items, so i have two items, yet when i have O X O, zero buckets of zero items... how can i suddenly have one item.... it makes no sense....

So that's my answer for why!

and I too thought we were talking programming which is why im here really... Glad I learned something

if post-title.content.firstglance != obvious-to-stupid-crazyfray thenirrelevant-pseudocode.add
end if

Lol Very good!, nice use of the 'Not equal to' version of != At least this topic has described both versions! Is there another i wonder?

[DeM0nFiRe 0]

Lol...you confused me greatly there. I thought you meant in programming terms, since ! is used to mean not...so while x=x (x is equal to itself), x!=y (x is not equal to y).

 

Which is why I thought 'what an idiot, asking why 0 isn't equal to 1'. More fool me!

 

if post-title.content.firstglance != obvious-to-stupid-crazyfray then

irrelevant-pseudocode.add

end if

Actually, 'x=x' would mean 'x becomes equal to itself.' a single equals is not a conditional operator, it's an assignement operator. The conditional is '=='

[DarkPsycho 0]

1 X 2 is the same as saying i have one bucket of two items, so i have two items, yet when i have O X O, zero buckets of zero items... how can i suddenly have one item.... it makes no sense....

0 x 0 doesn't equal 1

It equals 0. So, you don't suddenly have one item, you still have none.

 

This is kind of similar to x⁰ is equal to 1.

Edited December 6, 2007 by DarkPsycho (see edit history)

[crazyfray 0]

Actually, 'x=x' would mean 'x becomes equal to itself.' a single equals is not a conditional operator, it's an assignement operator. The conditional is '=='

True, but since != is always comparative (mainly since an additional equals sign (as in !== for does not equal) would be redundant, as you can't set a variable as being 'anything other than' a value) I didn't want to complicate things

 

Still, fair point.

 

EDIT: After all, these are mathematicians

Edited December 7, 2007 by crazyfray (see edit history)

[DeM0nFiRe 0]

Hehe, yeah. Mathematicians are like Junior Programmers

Edited December 7, 2007 by DeM0nFiRe (see edit history)

[Erdemir 0]

I think you havent known the factorial formula yet.

 

The factorial formula is

n! = integral[0 to infinity] (t^(n-1)) * e^(-t) * dt

 

Actually the formula is

Range is from negative infinity to positive infinity including all real numbers. Not as you know that from 0,1,2,3...infinity.

 

In this formula give z or n the value "0" and run the formula, it will give you the result "1".

 

 

http://forums.xisto.com/topic/48583-factorial/

[iGuest 3]

Why does 0!=1 - Why does i happen?

Why does 0!=1

 

Why should you be concerned that 0! =1? You may not even know what a factorial number is.

 

Reading the following you may come to understand the idea of a factorial. You may also be able to please your friends and confound your enemies by being able to show that 0! =1. Here is an explanation, requiring only knowledge of simple arithmetic to understand.

In general any factorial number (call it and!), may be written,

and! = and x (and-1) x (and-2) x (and-3) x ... X 2 x 1

This is the general definition of a factorial number.

If you want it in words; a factorial number is the product of all positive integers from 1 to the number under consideration.

The main place it is likely to be encountered is when considering those groups and arrangements of objects mentioned above.

So where does all this 0! Stuff fit in?

Nobody has trouble in stating 2! = 2 x 1 , or even that 1! = 1, but 0! Appears to make no sense.

 

It does however, have a value of 1. This is rather counter intuitive but arises directly from our general definition.

and! = and x (and-1) x (and-2) x (and-3) x ... X 2 x 1

Notice this may be written,

and! = and x (and-1)! Still exactly the same definition.

If the left hand side (LHS) = the right hand side (RHS) then dividing both sides by and should leave them still equal, so it is still true to write,

and!/and = and x (and-1)!/and

 

The (and-1)! in the RHS is being both multiplied by and and divided by and. These cancel leaving,

and!/and = (and-1)! If you doubt this, try it with real numbers, e.G. 4!/4 = 3! or (4 x 3 x 2 x 1)/4 = 3 x 2 x 1 = 6

The equation we now have is,

and!/and = (and-1)!

It is still our original definition in a rearranged form. For convenience I shall write it the other way round.

(and-1)! = and!/and

We also said that our factorial uses the positive integers 1 and above. Try the value of and=2 in our rearranged formula and we get,

(2-1)! = 2!/2 or 1! = 2x1/2

The RHS calculates to 1, so we have the statement 1!=1 That is what we guessed intuitively above. It is now confirmed. But look what happens when we substitute the legitimate value of and=1 in our formula.

(1-1)! = 1!/1

Evaluating this statement gives

0! = 1!/1

We have just shown 1!=1 so the RHS is 1/1 or 1.

Our rearranged definition of a factorial number gives directly the statement,

0!=1 Counter intuitive perhaps but if the definition is true then this is true.

Why not tell your friends about it? Help dispel the widespread ignorance about 0!

Did you understand something?

 

 

From: Muhammed Waqas

 

 

-reply by Muhammed Waqas