Sign up ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Assume that $a$, $b$ are real numbers. Prove that there exists integers $m$ and $n$ that satisfy $a < \frac{m}{2^n} < b$.

share|cite|improve this question

1 Answer 1

up vote 0 down vote accepted

Let $x=b-a$. Then $2^nb-2^na=2^nx$. Choose $n$ big enough to make $2^nx>1$. Then there is an integer, $m$, such that $2^na<m<2^nb$.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.