# Beginning mathematical proof

## Homework Statement

I originally made this thread for something else, but I have another problem that I need help with.

Suppose a and b are nonzero real numbers. Prove that if a < 1/a < b < 1/b then a < -1.

## Homework Equations

A hint was given for the problem: Assume a < 1/a < b < 1/b. Now prove that a < 0, and then use this fact to prove that a < -1.

Thanks

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For this problem, first think about what it means when $$a<\frac1a$$. What values could $$a$$ have? You should identify two possibilities (two open intervals where $$a$$ could be). The second part of the inequality will let you narrow it down to one.