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aortizmena
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Homework Statement
Prove that D={[tex]\frac{m}{2^{n}}[/tex] : n[tex]\in[/tex] N , m=0,1,2,...,2[tex]^{n}[/tex]} (dyatic rationals set) is dense on [0,1] , i.e. if (a,b) [tex]\subset[/tex] [0,1] then (a,b) [tex]\bigcap[/tex] D [tex]\neq[/tex] emptyset
Homework Equations
The Attempt at a Solution
Is it wrong if I just state that because a,b[tex]\in[/tex][tex]\Re[/tex] we know that there exists m,n[tex]\in[/tex]N, l=[tex]\frac{m}{2^{n+1}}[/tex], u=[tex]\frac{m}{2^{n-1}}[/tex] and r=[tex]\frac{m}{2^{n}}[/tex] such that l [tex]\leq[/tex] a [tex]\leq[/tex] r [tex]\leq[/tex] b [tex]\leq[/tex] u?
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