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Interlacing addition of ordinals

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378
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Can zero be in the least element in a proof of mathematical induction?

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283
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Prob. 5, Sec. 10, in Munkres' TOPOLOGY, 2nd ed: The well-ordering theorem implies the choice axiom

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121
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Prob. 8 (b), Sec. 10, in Munkres' TOPOLOGY, 2nd ed: The union of any collection of disjoint well-ordered sets indexed by some well-ordered set ...

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190
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Prob. 10 (a, b, c), Sec. 10, in Munkres' TOPOLOGY, 2nd ed: Let $J$ and $C$ be well-ordered sets such that . . .

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555
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What uncountable ordinals live in the long line?

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#general-topology #ordinals #well-orders
37.4k
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Is there a known well ordering of the reals?

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#set-theory #order-theory #axiom-of-choice #well-orders
512
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Showing that well-ordered subsets of $P(\omega)$ are countable

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1.2k
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questions about well-order

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#elementary-set-theory #relations #order-theory #well-orders
1.2k
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Explicit well-ordering of $\mathbb{N}^{\mathbb{N}}$

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#set-theory #well-orders
2.3k
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The well ordering principle

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#set-theory #real-numbers #well-orders
3.9k
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Totally ordering the power set of a well ordered set.

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513
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Existence of a particular well-ordering of [0,1]

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Isomorphism between well ordered sets

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3.9k
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A way to well-order real line

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#elementary-set-theory #axiom-of-choice #well-orders

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