Division by zero after removing factor.

Question

I know that anything divided by zero is undefined and I understand why. However, I have just discovered this sum, and it confused me greatly. Could anyone explain what is going on here:

$$x-x=0$$ $$x(1-1)=0$$ $$x=\frac{0}{(1-1)}$$ $$x=\frac{0}{0}$$

For example when 'x=3':

$$3-3=0$$ $$3(1-1)=0$$ $$3=\frac{0}{(1-1)}$$ $$3=\frac{0}{0}$$

If you know division by $0$ is undefined, why would you assume you're getting sane results, after dividing by $(1-1)$? — pjs36, Mar 22 '15 at 22:42

score 1 · Answer 1 · answered Mar 22 '15 at 23:41

1

Dividing a number by zero results in an undefined expression. This is true however you write zero. $\displaystyle 0, x - x,\cos \left({\frac \pi 2}\right),\ln 1, \text {etc.}$ all are the same number.

answered Mar 22 '15 at 23:41

GFauxPas

5,047

Division by zero after removing factor.

1 Answers1