Answer to Question #146710 in Real Analysis for Dolly

Question #146710
If A={x∈Q,x<3} then find Sup(A)
1
Expert's answer
2020-11-26T17:31:22-0500

Claim: sup(A)=3\sup(A)=3

Proof:


Clearly, by definition for all xAx\in A , x<sup(A)=3x<\sup(A)=3

Now, for every ϵ:=3x2>0\epsilon:=3-\frac{x}{2}>0 , 3ϵ=x2<x3-\epsilon=\frac{x}{2}<x <3<3, 3ϵ3-\epsilon is not an upper bound of AA. Hence done.


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