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  "body": "\n## Summary\n\nA constructive proof of an existence statement $\\exists x \\, P(x)$ gives a specific object $a$, or a method to find it, and proves $P(a)$.\nA non-constructive proof shows that an object exists without giving it, for example by [[proof by contradiction|0J0XBKG64S]].\n\n## Remarks\n\nA classical non-constructive example: there are irrational numbers $a$ and $b$ such that $a^b$ is rational. Consider $\\sqrt{2}^{\\sqrt{2}}$. It is rational or irrational, and each case gives such $a$ and $b$.\nIntuitionistic logic accepts only constructive proofs of existence.\n\n## Explanations\n\n### L1 human\n\nA constructive proof that a solution exists shows you the solution.\nA non-constructive proof only shows that \"no solution\" is impossible.\nBoth are correct in classical mathematics, but the constructive proof tells you more.\n",
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