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I originally made this thread for something else, but I have another problem that I need help with.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

Last edited:

Mark44
Mentor
For b, you're missing the inequality in the triangle inequality.

new problem bump

It's not like threads go in the landfill and pollute kindergarten playgrounds after we're done with them. No need to recycle. Make a new thread when you have a new problem.

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.