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  "body": "\n## Summary\n\nA semialgebraic set is a subset of $\\R^n$ described by finitely many polynomial equations and strict inequalities combined with \"and\", \"or\" and \"not\".\nBy the [[Tarski–Seidenberg theorem|3W5JGDZAN0]], the projection of a semialgebraic set is again semialgebraic.\nSemialgebraic sets have finitely many connected components and admit triangulations.\nThey are the natural objects of [[real algebraic geometry|PPWJ8NFH7G]] and the model example of an [[o-minimal structure|DTWHAW1N0V]].\n\n## Explanations\n\n### L1 human\n\nThe closed disc $x^2 + y^2 \\le 1$ is not the zero set of polynomials, but it is described by one polynomial inequality.\nSemialgebraic sets are all shapes obtained in this way from finitely many polynomial equations and inequalities.\nA half-plane, a triangle and the region between two parabolas are examples.\nThe graph of the sine function is not, because it crosses the axis infinitely often, while a polynomial description allows only finitely many such crossings.\n",
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