Question

Show that extension $\mathbb{R}(x) \supseteq \mathbb{R}$ is a real extension (ordered extension)

score 60 · Answer 1 · 2026-05-10 19:35:22

60

Views

Show that extension $\mathbb{R}(x) \supseteq \mathbb{R}$ is a real extension (ordered extension)

Published on 10 May 2026 - 19:35

score 58 · Answer 2 · 2026-04-14 09:14:14

58

Views

A property of $\gamma_1$ extensions of real closed fields.

Published on 14 Apr 2026 - 9:14

score 799 · Answer 3 · 2026-04-09 13:40:15

799

Views

show $1/x$ does not equal $ 0$

Published on 09 Apr 2026 - 13:40

score 322 · Answer 4 · 2026-04-12 23:23:33

322

Views

A Sequence which is co-Cauchy with a Positive Cauchy Sequence is Positive

Published on 12 Apr 2026 - 23:23

score 63 · Answer 5 · 2026-04-13 08:07:11

63

Views

To prove (2,2) is an interval in R

Published on 13 Apr 2026 - 8:07

score 110 · Answer 6 · 2026-04-11 17:51:19

110

Views

Relation between multiplicative and additive identity in an ordered field

Published on 11 Apr 2026 - 17:51

score 33 · Answer 7 · 2026-04-13 16:51:36

33

Views

Inductive sets in ordered field

Published on 13 Apr 2026 - 16:51

score 196 · Answer 8 · 2026-03-25 15:41:08

196

Views

Can the Dedekind completion of the hyperreal numbers be embedded in an ordered field?

Published on 25 Mar 2026 - 15:41

score 224 · Answer 9 · 2026-04-15 18:40:10

224

Views

Examining the theorem, for all $\epsilon \gt 0$, if $x \le y + \epsilon$, then $x \le y$

Published on 15 Apr 2026 - 18:40

score 86 · Answer 10 · 2026-04-12 11:32:30

86

Views

Total ordering on a field defined by a subset

Published on 12 Apr 2026 - 11:32

score 77 · Answer 11 · 2026-03-25 18:24:39

77

Views

Are order-preserving field embeddings unique?

Published on 25 Mar 2026 - 18:24

score 246 · Answer 12 · 2026-04-14 18:26:22

246

Views

How can we show that if $|x| \le 1/n$ for all natural numbers, n, then $x = 0$?

Published on 14 Apr 2026 - 18:26

score 49 · Answer 13 · 2026-04-17 09:28:46

49

Views

Is it true that if $p,q \in K_{>0}$, then $[0,pq) \subseteq [0,p)[0,q)$ in any ordered field?

Published on 17 Apr 2026 - 9:28

score 326 · Answer 14 · 2026-04-13 05:43:07

326

Views

Name and definition of the standard ordering on $\mathbb{R}$

Published on 13 Apr 2026 - 5:43

score 36 · Answer 15 · 2026-04-10 12:01:38

36

Views

Proof that the nonnegativy of squares does not follow from the rest of the prepositive cone definition

Published on 10 Apr 2026 - 12:01

List Question

Show that extension $\mathbb{R}(x) \supseteq \mathbb{R}$ is a real extension (ordered extension)

A property of $\gamma_1$ extensions of real closed fields.

show $1/x$ does not equal $ 0$

A Sequence which is co-Cauchy with a Positive Cauchy Sequence is Positive

To prove (2,2) is an interval in R

Relation between multiplicative and additive identity in an ordered field

Inductive sets in ordered field

Can the Dedekind completion of the hyperreal numbers be embedded in an ordered field?

Examining the theorem, for all $\epsilon \gt 0$, if $x \le y + \epsilon$, then $x \le y$

Total ordering on a field defined by a subset

Are order-preserving field embeddings unique?

How can we show that if $|x| \le 1/n$ for all natural numbers, n, then $x = 0$?

Is it true that if $p,q \in K_{>0}$, then $[0,pq) \subseteq [0,p)[0,q)$ in any ordered field?

Name and definition of the standard ordering on $\mathbb{R}$

Proof that the nonnegativy of squares does not follow from the rest of the prepositive cone definition

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