Let B= {a + b√2 + c√3+ d√5: a,b,c,d ∈ Q} . Does B possess the least upper bound property?

I know that B will have the least upper bound property if every non-empty subset of B which is bounded from above has a supremum in B. However, I am a bit lost on how to go about showing this.

I let S = {x ∈ Q: x^2 ≤ 7} be a subset of B. Now S has an upper bound in B but does not have a supremum in Q since no values of a + b√2 + c√3+ d√5 = √7 exists for a, b, c, d ∈ Q.

Is this correct?

2017-04-11T00:37:33.809Z

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