prove that zero factorial is equal to 1? ,0!=1 & 1!=1. can we say that 0=1?

Answer 1

2! = 3! / 3 = 2
1! = 2! / 2 = 1
0! = 1! / 1 = 1

No, 0 doesn't equal 1.

Answer 2

For +ve Numbers [i-e, Natural numbers], we define n! as:
n!=n.(n-1).(n-2).(n-3)..........3.2.1
Actually, when we proceed towards right, we multiply the first number with a number which is less than unity. You can see above that n is multiplied by n-1, and n-1 is multiplied by n-1-1=n-2, and so on. Using this principle, we can Proceed to Show that 0!=1
For a -ve number its factorial approaches to infinity...i-e:
(-1)!=(-1).(-1-1).(-1-1-1).(-1-1-1-1).................. up to ∞ factors.
OR
(-1)!=(-1).(-2).(-3).(-4).........up to ∞ factors.
So, we can write as, (-1)=∞ ... (1)
Now,
0!=0(-1)(-2)..........
=0.(-1)!
From eq. (1)
0!=0.∞ .......(2)
Now, Product of zero and infinity equals to 1,i-e:
1/0=∞
Or 1=0.∞ ......(3)
Using eq. (3) in (2), we get:
0!=1
Hence, Proved.....
This proof is without ambiguity. Some authors prove it in more simpler way:
We know that:
n!=n.(n-1)!
OR
n!/n=(n-1)! ........ (4)
Now, put n=1 in equation number (4), we get:
1!/1=(1-1)!
OR
1!=0!
OR
0!=1
Hence, this is the second Proof..

Answer 3

0 1 Proof

Answer 4

There is a split function definition for factorial function. Meaning we cannot define a function by just saying that "when you factorial you multiply all integers from 1 to that number" but then how are you going to compute for 0!.

We define the "factorial function", and we notice the recursive identity:
x! = x · (x - 1)!

If x = 1, then
1! = 1 · 0!

And
1 · 0! = 1!
0! = 1!
0! = 1


Here we cannot define the values for negative integers, such as when x = 0,
x! = x (x - 1)!

0! = 0 (0 - 1)!
(-1)! = 0!/0
(-1)! = 1/0 = ±∞

^_^

Answer 5

well, 0!=1 and 1!=1 implies 0!=1!, but you can't just remove the ! from both sides (like if you had 2^2=(-2)^2 doesn't imply 2=-2). It's not a one to one function in this case. My way of understanding why 0!=1 is because there is 1 way to arrange 0 objects - by not arranging them at all.

Answer 6

2 x 2=4 but also (-2) x (-2)=4, so do we say 2= -2? If 0=-1 was true, why would we care to give them different names? Is there life after death?

Answer 7

te aboove answers my Dr.Math is amazing but I would like to present a verbal kind of proof. Factrial genrally means permutions of objects. If there are 3 objects you can arrange them in 6 different ways. But if there are no objects, then there is only one way, that is leave the place empty. Hence 0! is 1.

Answer 8

hi tasneem_a
your question has been answered correctly by "demiurge4" and "kevin!"
i am answering your question just to get points.

we know that,
n! = n.(n-1)(n-2)....3.2.1
i.e. n! = n.(n-1)!
i.e. (n!/n) = (n-1)!

now substituting n =1 in the above equation

(1!/1) = (1-1)!
i.e. 1 = 0!

this is the required proof of 0! = 1

Answer 9

Visit this Link: http://mathematicbrain.blogspot.com/2014/11/proof-01.html

Answer 10

Obviously,1!=1.For 0!=1 or 0=1,
take two variables,x and y.
let x=y,
multiply both sides with x,
x.x=x.y
x.x-x.y=0
x(x-y)=0
1=0/x(x-y)
Hence,1=0.