The value of 0/0

Now,

we know one thing

n!=n(n-1)(n-2)......

now,

n!=n[(n-1)!]

n!/n=(n-1)!

now we take n=1,

1!/1=(1-1)!

0!=1 [Equation 1]

In the same way take n=0

so

(0-1)!=0!/0 [n!/n= n(n-1)(n-2)(n-3)...]

(-1)!=infinity [Equation 2] (1/0 assumes the value of infinity)

{We are getting the right answer as factorial of a negative number does not exist}

Now think how 0!=1

Now if we can write 2!=2*1

then we should try writing 0! in the same way.

so we write,

0!=0(-1)(-2)(-3)(-4)*....(till infinity)

0!=0*[(-1)!] {Take n=-1 in n(n-1)(n-2).....}

0!=infinity*0

{Now we assume that infinity is a large number so zero multiplied by a large number is also zero)

we get 0!=0 [Equation 3]

Compare Equation 1 & 3

we get 1=0

which is WRONG

so we take infinity =n/0 [ where 'n' is any real number]

We get,

(infinity) *0 = (n/0) *0

=0/0 [Equation 4]

Now Compare Equation 1 & 4

we get 0/0=1.

Note by Vipul Maisske
5 years, 2 months ago

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Bro nice try..

- 4 years, 12 months ago

Ty bro :)

- 4 years, 12 months ago