Q10. Let x > 1 bea positive real numberandr a positive irrational number. The LUB is the union of the two elements. The union of two elements is an upper bound for them, because for any two sets S and T, S ⊆ S ∪ T. If x ∈ (0,1), then xr is 1 (1/x)r. A short summary of this paper. Weimin Chen. Before proving the following Lemma, let us recall [3] that if A is any subset of a partially ordered set then (2) lubA = glb U where U is the set of all the upper bounds of A and where lub and glb stand respect,ively for the least upper bound and the greatest lower bound. The xr is the lub of the set {xp | p ∈ Q,0 < p < r}. If the LUB and GLB exist for all S P, then hP;

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