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  "body": "\n## Summary\n\nThe general recursive functions, also called $\\mu$-recursive functions, are the functions on the natural numbers obtained from the [[primitive recursive functions|5NVA2JRHPV]] by adding unbounded search.\nThe search operator $\\mu$ returns the least number at which a given function takes the value $0$, and may run forever.\nSo the class contains partial functions, and the total ones among them are exactly the total [[computable functions|KZSB5E471K]].\nThis class was one of the first precise definitions of computability, and it agrees with computability by [[Turing machines|758EYCN27B]].\n\n## Explanations\n\n### L1 human\n\nPrimitive recursion is like a for-loop: the number of steps is known before the loop starts.\nUnbounded search is like a while-loop: keep trying $y = 0, 1, 2, \\ldots$ until a condition holds.\nA while-loop may never stop, and then the function has no value at that input.\nFor example, searching for the least $y$ with $y^2 \\ge x$ always stops and gives the rounded-up square root of $x$.\nAdding this one tool to bounded loops gives every computable function.\n",
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