Question

Does surreal numbers with bounded birthdays form a field?

score 169 · Answer 1 · 2026-03-25 17:51:57

169

Views

Does surreal numbers with bounded birthdays form a field?

Published on 25 Mar 2026 - 17:51

score 374 · Answer 2 · 2022-02-11 01:01:14

374

Views

$K$ is an ordered field $\leftrightarrow$ Subset $P \subseteq K$ exists with certain characteristics

Published on 11 Feb 2022 - 1:01

score 181 · Answer 3 · 2022-02-11 04:43:03

Is every field of characteristic zero whose nonzero elements are squares or the additive inverse of squares but not both a Euclidean ordered field?

score 67 · Answer 4 · 2022-02-12 20:34:58

67

Views

Show that a field of rational expressions with real coefficients is ordered.

Published on 12 Feb 2022 - 20:34

score 175 · Answer 5 · 2022-02-12 23:34:32

175

Views

Least upper bound of $\{x\in\mathbb{R}:x^2<2\}$

Published on 12 Feb 2022 - 23:34

score 1.3k · Answer 6 · 2022-03-15 20:36:58

1.3k

Views

Prove all 4 axioms of "less than" are necessary (for real numbers)

Published on 15 Mar 2022 - 20:36

score 129 · Answer 7 · 2022-04-08 00:13:10

129

Views

Is this way of writing the Field and Order Axioms correct?

Published on 08 Apr 2022 - 0:13

score 192 · Answer 8 · 2022-05-11 19:20:51

192

Views

$F(\sqrt d)$ is an ordered field

Published on 11 May 2022 - 19:20

score 38 · Answer 9 · 2022-06-12 05:53:22

38

Views

Question about axioms of an ordered field.

Published on 12 Jun 2022 - 5:53

score 165 · Answer 10 · 2022-06-18 10:57:31

165

Views

Let $(F,+,\cdot,0_F,1_F,\le)$ be an ordered field. If the set $\{x\in F: 0_F\le x\le 1_F\}$ is complete, is the whole field complete?

Published on 18 Jun 2022 - 10:57

score 207 · Answer 11 · 2026-03-25 20:41:27

207

Views

Can the hyper hyper real numbers be constructed?

Published on 25 Mar 2026 - 20:41

score 283 · Answer 12 · 2026-03-25 17:37:50

283

Views

Can the surreal numbers be completed to form an ordered field?

Published on 25 Mar 2026 - 17:37

score 52 · Answer 13 · 2022-06-29 07:51:31

52

Views

Whether some positive sequence approaches 0 in any ordered field

Published on 29 Jun 2022 - 7:51

score 80 · Answer 14 · 2022-06-29 22:30:58

80

Views

Can the hyperreal numbers have a property akin to completeness by considering hypernatural sequences?

Published on 29 Jun 2022 - 22:30

score 117 · Answer 15 · 2022-07-11 19:32:44

117

Views

Convex subring is local

Published on 11 Jul 2022 - 19:32

List Question

Does surreal numbers with bounded birthdays form a field?

$K$ is an ordered field $\leftrightarrow$ Subset $P \subseteq K$ exists with certain characteristics

Is every field of characteristic zero whose nonzero elements are squares or the additive inverse of squares but not both a Euclidean ordered field?

Show that a field of rational expressions with real coefficients is ordered.

Least upper bound of $\{x\in\mathbb{R}:x^2<2\}$

Prove all 4 axioms of "less than" are necessary (for real numbers)

Is this way of writing the Field and Order Axioms correct?

$F(\sqrt d)$ is an ordered field

Question about axioms of an ordered field.

Let $(F,+,\cdot,0_F,1_F,\le)$ be an ordered field. If the set $\{x\in F: 0_F\le x\le 1_F\}$ is complete, is the whole field complete?

Can the hyper hyper real numbers be constructed?

Can the surreal numbers be completed to form an ordered field?

Whether some positive sequence approaches 0 in any ordered field

Can the hyperreal numbers have a property akin to completeness by considering hypernatural sequences?

Convex subring is local

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