(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let A be a non empty subset of R that is bounded above

Set D:={2a|a (belongs to) A}

Is it necessarily true that the sup D = 2 sup A? Either prove or provide a counterexample.

2. Relevant equations

The completeness axiom

3. The attempt at a solution

I am seriously clueless on how to approach... but I still tried something

Let sup D = y and sup A = x

d=2a; d<=y; a<=x

or can I say choose a as the largest value in A, so 2a=d is the largest value in D. Since both are the upper bound for each set and for all upper bound and real number, they are the smallest. so, d is sup D and a is sup A.

Therefore, d=2a => sup D = 2 sup A

But these method seems a bit weird...

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# Proving on the completeness theorem of real number

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