Consider the set B of all dyadic rational numbers between 0 and 1. Show that for all a in [0,1], there exists for epsilon>0, there exists at least one c in the set B such that abs(a-c)<epsilon.

Could someone help me prove this?

Thanks.

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- Oct 30th 2006, 04:11 PMAlexis15Dyadic Rational Number
Consider the set B of all dyadic rational numbers between 0 and 1. Show that for all a in [0,1], there exists for epsilon>0, there exists at least one c in the set B such that abs(a-c)<epsilon.

Could someone help me prove this?

Thanks.