Answer to Question #3409 in Real Analysis for junel

Question

Show that if a > 0, then (1/a) > 0 and (1/(1/a)) = a.

Answer 1

It's evident that
1 > 0.
Let's divide both sides of inequality by positive number a:
1/a > 0 / a
1/a > 0.


<img src="/cgi-bin/mimetex.cgi?%5Cfrac%7B1%7D%7B%5Cfrac%7B1%7D%7Ba%7D%7D%20=1%5Cfrac%7Ba%7D%7B1%7D%20=%20a" title="\frac{1}{\frac{1}{a}} =1\frac{a}{1} = a">