Why is $\frac{1}{\frac{1}{X}}=X$? Can someone help me understand in basic terms why $$\frac{1}{\frac{1}{X}} = X$$
And my book says that "to simplify the reciprocal of a fraction, invert the fraction"...I don't get this because isn't  reciprocal by definition the invert of the fraction? 

Naturally, if we inverse some inverted object, we will have the object itself!
This matter take place for numbers and their operations:
$$-(-x)=x$$
and for any non-zero $x$ $$\frac{1}{\frac{1}{x}}=x$$
(if we know "our limits" this fact is true for all objects in mathematics also for functions $(f^{-1})^{-1}=f$, directions(vectors, matrices, ...) and so on.)
