I found this in some other website, its basically the manipulation of a formula to finally give 1=0!. Here it is:

Let x = 1

Then, x^2=x

x^2-1 = x-1

Dividing both sides by (x-1), we get

x+1 = 1

x+1-1 = 0, so

Since x=1,

1=0

Any explanations?

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- Jun 20th 2011, 05:02 AMIBstudentIs 1 equal to 0?
I found this in some other website, its basically the manipulation of a formula to finally give 1=0!. Here it is:

Let x = 1

Then, x^2=x

x^2-1 = x-1

Dividing both sides by (x-1), we get

x+1 = 1

x+1-1 = 0, so

Since x=1,

1=0

Any explanations? - Jun 20th 2011, 05:03 AMQuackyRe: Is 1 equal to 0?
- Jun 20th 2011, 05:05 AMearbothRe: Is 1 equal to 0?
- Jun 20th 2011, 05:07 AMProve ItRe: Is 1 equal to 0?
You are correct that $\displaystyle \displaystyle 1 = 0!$, but $\displaystyle \displaystyle 1 \neq 0$.

$\displaystyle \displaystyle \begin{align*} n! &= n(n - 1)! \\ \frac{n!}{n} &= (n - 1)! \end{align*}$

Now letting $\displaystyle \displaystyle n = 1 $ we have

$\displaystyle \displaystyle \begin{align*} (1-1)! &= \frac{1!}{1} \\ 0! &= \frac{1}{1} \\ 0! &= 1 \end{align*}$ - Jun 20th 2011, 05:09 AMQuackyRe: Is 1 equal to 0?
- Jun 20th 2011, 05:19 AMSorobanRe: Is 1 equal to 0?

$\displaystyle \boxed{\begin{array}{c}\text{Theorem} \\[2mm]1 = 0\:\text{ for large values of }0.\end{array}}$