Let F be ordered field, A ⊆ F, and α ∈ F. Show that α = glbA if and only if (−∞,α) ∩ A = ∅, and for all β > α, [α,β) ∩ A

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answerhappygod
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Let F be ordered field, A ⊆ F, and α ∈ F. Show that α = glbA if and only if (−∞,α) ∩ A = ∅, and for all β > α, [α,β) ∩ A

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Let F be ordered field, A ⊆ F, and α ∈ F. Show that α = glbA ifand only if (−∞,α) ∩ A = ∅, and for all β > α, [α,β) ∩ A 6 !=∅.
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