Is this a correct expression of the aramuseum.orgematical statement, "Every confident real number has precisely two square roots.";

expression: ∀x∃a∃b((x>0) → (a!=b)∧(x=$a^2$)∧(x=$b^2$)).

You are watching: Every positive number has two square roots


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The explain as written is true, yet doesn"t capture the indigenous "exactly". Additionally, her quantification is a little odd: I"d have expected that to review $$(\forall x)(x>0 \to \exists a \exists b \dots)$$because (while yours is true) it"s a bit much more work to check that yours yes, really is true in the instance that $x \leq 0$.

I"m going to use several various shapes of base to shot to make this much easier to read, yet they"re all simply brackets.To record "exactly", you want $$(\forall x)\left 0 \to \left<(\exists a)(\exists b) \(a \not = b) \wedge (a^2 = x) \wedge (b^2 = x) \colorred \wedge (\forall c) \colorred \left((c^2 = x) \to \right) \ \right> \right>$$


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