How do we write the following in predicate logic?
The equation $ x^{2} + 2x + 1 = 0 $ has no solutions over the natural numbers.
2026-03-29 14:06:43.1774793203
How to write "The equation $ x^{2} + 2x + 1 = 0 $ has no solutions over the natural numbers" in predicate logic
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\begin{align} & \forall x\ (x\in\mathbb N \rightarrow \lnot ( x^2+2x+1 = 0)) \\[12pt] \text{or } & \lnot\exists x\ (x\in \mathbb N \wedge x^2+2x+1=0) \end{align} or other simple variants of these.