Question

Every subset of a well-ordered set is identical to a union of intervals of the set.

score 112 · Answer 1 · 2017-10-23 08:50:24

112

Views

Every subset of a well-ordered set is identical to a union of intervals of the set.

Published on 23 Oct 2017 - 8:50

score 1.1k · Answer 2 · 2017-10-26 21:57:41

1.1k

Views

Well-Ordering Principle Let S be a nonempty subset of $\{n \in \mathbb{Z}: n \le 0\}$

Published on 26 Oct 2017 - 21:57

score 539 · Answer 3 · 2017-11-06 00:03:37

539

Views

Prove that no ordinal is an element of itself

Published on 06 Nov 2017 - 0:03

score 109 · Answer 4 · 2017-11-06 12:49:39

109

Views

Why is the Mitchell order well-founded?

Published on 06 Nov 2017 - 12:49

score 246 · Answer 5 · 2017-11-07 21:33:42

246

Views

Does the proof of the well-ordering principle not commit the circular reasoning fallacy?

Published on 07 Nov 2017 - 21:33

score 239 · Answer 6 · 2017-11-08 10:18:28

239

Views

When is minimal element $=$ least element?

Published on 08 Nov 2017 - 10:18

score 141 · Answer 7 · 2017-11-09 12:58:34

141

Views

What is a good argument that for well-ordered subsets it is more reasonable to take initial segments rather than arbitrary subsets?

Published on 09 Nov 2017 - 12:58

score 3.1k · Answer 8 · 2017-11-10 13:04:56

3.1k

Views

Well-Ordering of the Natural Numbers

Published on 10 Nov 2017 - 13:04

score 39 · Answer 9 · 2017-11-21 15:29:15

39

Views

Alternative definition o a well order

Published on 21 Nov 2017 - 15:29

score 256 · Answer 10 · 2017-11-22 20:13:45

256

Views

A certain subset of a well-ordered uncountable set empty or not?

Published on 22 Nov 2017 - 20:13

score 473 · Answer 11 · 2017-12-02 04:05:14

473

Views

Ordinal comparison trichotomy

Published on 02 Dec 2017 - 4:05

score 1.7k · Answer 12 · 2026-03-26 11:01:15

1.7k

Views

Every well-ordering is isomorphic to the set of all lesser ordinals under ordinal comparison

Published on 26 Mar 2026 - 11:01

score 388 · Answer 13 · 2017-12-12 23:23:30

388

Views

How to prove well-ordering?

Published on 12 Dec 2017 - 23:23

score 76 · Answer 14 · 2017-12-13 09:47:44

76

Views

What is the difference between constructing and axiomatizing a well-ordering?

Published on 13 Dec 2017 - 9:47

score 226 · Answer 15 · 2026-02-23 15:30:50

226

Views

Separating Closed Sets in a Well-Ordered Set in the Order Topology

Published on 23 Feb 2026 - 15:30

List Question

Every subset of a well-ordered set is identical to a union of intervals of the set.

Well-Ordering Principle Let S be a nonempty subset of $\{n \in \mathbb{Z}: n \le 0\}$

Prove that no ordinal is an element of itself

Why is the Mitchell order well-founded?

Does the proof of the well-ordering principle not commit the circular reasoning fallacy?

When is minimal element $=$ least element?

What is a good argument that for well-ordered subsets it is more reasonable to take initial segments rather than arbitrary subsets?

Well-Ordering of the Natural Numbers

Alternative definition o a well order

A certain subset of a well-ordered uncountable set empty or not?

Ordinal comparison trichotomy

Every well-ordering is isomorphic to the set of all lesser ordinals under ordinal comparison

How to prove well-ordering?

What is the difference between constructing and axiomatizing a well-ordering?

Separating Closed Sets in a Well-Ordered Set in the Order Topology

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