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Hi I am trying some proofs and I am stuck on this one. It says to...

Hi I am trying some proofs and I am stuck on this one. It says to prove or give a counter example. For each real number p, there exist real numbers q and r such that qsin(r/5) =p.

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Answer #1

Doubt in this then comment below.. i will help you..

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Please thumbs up for this solution..thanks..

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Note one thing that value of sin is in between -1 to 1 ...

So, here sin(r/5) = p/q ....

So we take q such that p/q lies between -1 and 1 ...

So, for p positive , we take q is greater than p

And for p negative , we take q is less than p ....

Such that above condition hold ...

That means sin(r/5) exist ... Therefore , value of r also exist ...

So for each p in real number .. there exist real numbers q and r such that qsin(r/5) = p ....

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