Inequality (mathematics)
Sharp inequalities

An inequality is said to be sharp if it cannot be relaxed and still be valid in general. Formally, a universally quantified inequality φ is called sharp if, for every valid universally quantified inequality ψ, if ψ ⇒ φ holds, then ψ ⇔ φ also holds. For instance, the inequality ∀ a ∈ R. a ≥ 0 is sharp, whereas the inequality ∀ a ∈ R. a ≥ −1 is not sharp.
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