go on...
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In classical set theory, X is a proper class is for every level of the von Neumann hierarchy, there is an element of X beyond that level. This is reminiscent of the fact that for every way of encoding real numbers, you can produce a more expressive way of encoding reals.
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It's also literally true in the minimal model of Kripke-Platek set theory with infinity.
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I thought it isn’t.
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In classical set theory (ie models of ZFC), you're right; ℝ is a set. But see my replies to benzrf.
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