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  "body": "\n## Summary\n\nConstructive analysis is mathematical analysis carried out under the principles of [[constructivism|G958EQ8CWW]].\n[[Real numbers|08J2M1JYAG]] are given by [[Cauchy sequences|0PWX18FM4G]] of rationals with an explicit rate of convergence, and every existence proof must give an approximation method.\nBishop's book \"Foundations of Constructive Analysis\" of 1967 showed that a large part of classical analysis can be developed in this way.\nIts theorems are also valid classically, and they carry algorithms.\n\n## Explanations\n\n### L1 human\n\nIn constructive analysis, a real number is something you can compute to any accuracy you ask for.\nSome classical facts then need care.\nFor example, you cannot always decide whether a real number is zero, since you may never see a nonzero digit.\nSo the [[intermediate value theorem|00KAFBR32E]] is replaced by a version that finds a point where the function is as close to zero as you like.\nResults like this are often what a computation can actually deliver.\n",
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