Question

Verifying Proof: If $L$ is a poset with a bottom element, and $\exists \sup(S)$ for every subset $S \subset L$, then $L$ is a complete lattice

score 86 · Answer 1 · 2026-04-15 20:30:12

86

Views

Verifying Proof: If $L$ is a poset with a bottom element, and $\exists \sup(S)$ for every subset $S \subset L$, then $L$ is a complete lattice

Published on 15 Apr 2026 - 20:30

score 153 · Answer 2 · 2026-04-14 19:07:57

153

Views

Existence of Total Order Compatible with Partial Order

Published on 14 Apr 2026 - 19:07

score 312 · Answer 3 · 2026-04-14 10:55:48

312

Views

Uncountable chains in an uncountable partially ordered set

Published on 14 Apr 2026 - 10:55

score 140 · Answer 4 · 2026-04-13 11:42:18

140

Views

Existence of a non-trivial subgroup related by containment with the rest of subgroups

Published on 13 Apr 2026 - 11:42

score 56 · Answer 5 · 2026-04-12 01:57:57

56

Views

Is the growth of a function discrete?

Published on 12 Apr 2026 - 1:57

score 222 · Answer 6 · 2026-04-11 21:35:14

222

Views

What's wrong with this proof that $\mathbb{R}$ cannot be well-ordered?

Published on 11 Apr 2026 - 21:35

score 34 · Answer 7 · 2026-04-15 08:35:15

34

Views

Prove that $a$ is minimum of $B$ in $R^{-1}$ if and only if $a$ is maximum of $B$ in $R$.

Published on 15 Apr 2026 - 8:35

score 73 · Answer 8 · 2026-04-10 18:46:20

73

Views

Confusion in the statement of Zorn's Lemma

Published on 10 Apr 2026 - 18:46

score 92 · Answer 9 · 2026-04-12 08:35:27

92

Views

Proof that Order Sum Addition is Associative

Published on 12 Apr 2026 - 8:35

score 307 · Answer 10 · 2026-04-10 04:46:39

307

Views

General definition of antilexicographic order on arbitrary indexed family of ordered sets

Published on 10 Apr 2026 - 4:46

score 148 · Answer 11 · 2026-04-10 15:09:55

148

Views

About two definitions of a complete lattice. ("Introduction to Set Theory and Topology" by Kazuo Matsuzaka)

Published on 10 Apr 2026 - 15:09

score 40 · Answer 12 · 2026-04-14 16:43:06

40

Views

How to compute all equivalence classes of weight assignments to the vertices of a poset on n points that sum to m?

Published on 14 Apr 2026 - 16:43

score 118 · Answer 13 · 2026-04-13 17:45:42

118

Views

Why does the back and forth method fail to prove that, for each cardinality, any dense linear order without endpoints is unique up to isomorphism?

Published on 13 Apr 2026 - 17:45

score 56 · Answer 14 · 2026-04-15 13:56:53

56

Views

Determine an infinite subset $X \subseteq \mathbb{Z}_{\gt 1}$ such that $S \cap (X \times X)$ is a total order on $X$

Published on 15 Apr 2026 - 13:56

score 42 · Answer 15 · 2026-04-10 19:22:48

42

Views

Linear Order on Polish spaces

Published on 10 Apr 2026 - 19:22

List Question

Verifying Proof: If $L$ is a poset with a bottom element, and $\exists \sup(S)$ for every subset $S \subset L$, then $L$ is a complete lattice

Existence of Total Order Compatible with Partial Order

Uncountable chains in an uncountable partially ordered set

Existence of a non-trivial subgroup related by containment with the rest of subgroups

Is the growth of a function discrete?

What's wrong with this proof that $\mathbb{R}$ cannot be well-ordered?

Prove that $a$ is minimum of $B$ in $R^{-1}$ if and only if $a$ is maximum of $B$ in $R$.

Confusion in the statement of Zorn's Lemma

Proof that Order Sum Addition is Associative

General definition of antilexicographic order on arbitrary indexed family of ordered sets

About two definitions of a complete lattice. ("Introduction to Set Theory and Topology" by Kazuo Matsuzaka)

How to compute all equivalence classes of weight assignments to the vertices of a poset on n points that sum to m?

Why does the back and forth method fail to prove that, for each cardinality, any dense linear order without endpoints is unique up to isomorphism?

Determine an infinite subset $X \subseteq \mathbb{Z}_{\gt 1}$ such that $S \cap (X \times X)$ is a total order on $X$

Linear Order on Polish spaces

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