# Answer to Question #3409 in Real Analysis for junel

Question #3409

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

Expert's answer

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">

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">

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