Question

Proving if an element of an ordered field has a square root and is not 0, then it has exactly two square roots, one positive and one negative

score 491 · Answer 1 · 2019-06-30 04:29:50

491

Views

Proving if an element of an ordered field has a square root and is not 0, then it has exactly two square roots, one positive and one negative

Published on 30 Jun 2019 - 4:29

score 367 · Answer 2 · 2026-03-25 06:11:59

367

Views

A "complete" ordered field of ordinals

Published on 25 Mar 2026 - 6:11

score 146 · Answer 3 · 2019-08-12 08:03:20

146

Views

Given an arbitrary ordered field (F,<), is there always a sequence of strictly positive elements of F that tends to zero?

Published on 12 Aug 2019 - 8:03

score 240 · Answer 4 · 2019-08-18 04:16:15

240

Views

How can the hypernaturals be constructed from the naturals (or integers/ hyperintegers)

Published on 18 Aug 2019 - 4:16

score 72 · Answer 5 · 2019-08-23 23:56:38

72

Views

Proof that for any $a>1$, $a^n > 1 +na$ for sufficiently large $n$

Published on 23 Aug 2019 - 23:56

score 45 · Answer 6 · 2026-02-23 02:38:01

45

Views

Does every Archimedian partially ordered division ring embed in the reals?

Published on 23 Feb 2026 - 2:38

score 256 · Answer 7 · 2026-02-23 13:43:10

256

Views

Axioms of order in geometry and ordered fields

Published on 23 Feb 2026 - 13:43

score 129 · Answer 8 · 2019-09-19 09:13:46

129

Views

Find a transfinite monotone subsequence.

Published on 19 Sep 2019 - 9:13

score 446 · Answer 9 · 2019-09-20 20:27:49

446

Views

The Order of sets like $\mathbb Q$ and Justification of the Number Line

Published on 20 Sep 2019 - 20:27

score 178 · Answer 10 · 2019-09-27 23:56:47

178

Views

Prove that there exists no such total order

Published on 27 Sep 2019 - 23:56

score 46 · Answer 11 · 2019-09-30 14:06:05

46

Views

Is it useful that $k(X)$ is an ordered field if $k$ either is?

Published on 30 Sep 2019 - 14:06

score 104 · Answer 12 · 2014-03-13 04:13:52

104

Views

Unicity of order/positives in ordered field

Published on 13 Mar 2014 - 4:13

score 417 · Answer 13 · 2014-04-22 16:10:59

417

Views

Density of rationals in an ordered field

Published on 22 Apr 2014 - 16:10

score 99 · Answer 14 · 2014-05-22 09:58:07

99

Views

Exercise 5 .39 page 46 Real and Abstract Analysis [Hewitt and Stromberg]

Published on 22 May 2014 - 9:58

score 68 · Answer 15 · 2014-06-07 01:44:06

68

Views

Models of ZFC as Ordered Fields

Published on 07 Jun 2014 - 1:44

List Question

Proving if an element of an ordered field has a square root and is not 0, then it has exactly two square roots, one positive and one negative

A "complete" ordered field of ordinals

Given an arbitrary ordered field (F,<), is there always a sequence of strictly positive elements of F that tends to zero?

How can the hypernaturals be constructed from the naturals (or integers/ hyperintegers)

Proof that for any $a>1$, $a^n > 1 +na$ for sufficiently large $n$

Does every Archimedian partially ordered division ring embed in the reals?

Axioms of order in geometry and ordered fields

Find a transfinite monotone subsequence.

The Order of sets like $\mathbb Q$ and Justification of the Number Line

Prove that there exists no such total order

Is it useful that $k(X)$ is an ordered field if $k$ either is?

Unicity of order/positives in ordered field

Density of rationals in an ordered field

Exercise 5 .39 page 46 Real and Abstract Analysis [Hewitt and Stromberg]

Models of ZFC as Ordered Fields

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