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"

Proof:


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

Now, for every "\\epsilon:=3-\\frac{x}{2}>0" , "3-\\epsilon=\\frac{x}{2}<x" "<3", "3-\\epsilon" is not an upper bound of "A". Hence done.


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