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