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  "body": "\n## Summary\n\nThe axiom schema of replacement is a list of axioms of [[Zermelo–Fraenkel set theory|0HE5WDQ9FJ]], one for each formula.\nIt says that the image of a [[set|0BSJ7RQ9BW]] under a definable [[function|0EPAT51DXQ]] is again a set.\nFraenkel and Skolem proposed it in 1922 as an addition to Zermelo's axioms.\nIt is needed to build large sets such as $\\aleph_\\omega$ and to define functions on [[ordinals|0YSCSX5YZC]] by transfinite recursion.\n\n## Explanations\n\n### L1 human\n\nSuppose you have a set, and a rule that assigns to each element of it a unique object.\nReplacement says that the objects you get form a set too.\nYou replace each element by its image, and the result is still a set.\nFor example, from the set of natural numbers $\\N$ and the rule $n \\mapsto \\mathcal{P}^n(\\N)$, the $n$-fold power set, one gets the set $\\set{\\N, \\mathcal{P}(\\N), \\mathcal{P}(\\mathcal{P}(\\N)), \\dots}$.\nWithout replacement, this set cannot be proved to exist.\n",
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