Question

Existence and uniqueness up to isomorphism of the real numbers from axioms

score 1.9k · Answer 1 · 2014-07-09 09:54:42

1.9k

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Existence and uniqueness up to isomorphism of the real numbers from axioms

Published on 09 Jul 2014 - 9:54

score 464 · Answer 2 · 2014-07-17 16:14:35

464

Views

Ordered field with nested intervals axiom without Archimedean axiom

Published on 17 Jul 2014 - 16:14

score 357 · Answer 3 · 2014-07-21 23:14:32

357

Views

Proof that all ordered fields are in the Surreals

Published on 21 Jul 2014 - 23:14

score 475 · Answer 4 · 2014-08-07 19:55:09

475

Views

Are order isomorphic real closed fields isomorphic?

Published on 07 Aug 2014 - 19:55

score 248 · Answer 5 · 2014-08-21 03:38:27

248

Views

Replacing the "if $x ≤ y$, then $x + z ≤ y + z$" axiom in Reals.

Published on 21 Aug 2014 - 3:38

score 45 · Answer 6 · 2014-08-28 13:34:00

45

Views

In an Archimedian Field $F$, there is a positive rational element $r$ such that $r < z$ for any $ z>0$ in $F$

Published on 28 Aug 2014 - 13:34

score 37 · Answer 7 · 2014-08-28 15:24:27

37

Views

If $y,z$ are elements of an archimedean field $F$ and if $y<z$, then there is a rational element $r$ of $F$ such that $y<r<z$

Published on 28 Aug 2014 - 15:24

score 878 · Answer 8 · 2014-08-29 22:52:04

Prove that if $F$ is an ordered field in which every non empty set which has an upper bound also has a supremum , then $F$ is archimedean

score 2.3k · Answer 9 · 2014-09-10 18:45:05

2.3k

Views

Is 1/2 less than 1?

Published on 10 Sep 2014 - 18:45

score 938 · Answer 10 · 2014-09-24 00:32:57

938

Views

Proving Properties in Ordered Fields

Published on 24 Sep 2014 - 0:32

score 213 · Answer 11 · 2014-09-25 16:56:46

213

Views

Is$\ +\infty$ greater than any other number (surreal, superreal, hyperreal, ...)?

Published on 25 Sep 2014 - 16:56

score 3k · Answer 12 · 2014-10-06 22:36:14

3k

Views

How to prove: If $x \geq 0 $ and $x \leq \epsilon$, for all $\epsilon > 0$, then $x = 0$?

Published on 06 Oct 2014 - 22:36

score 50 · Answer 13 · 2014-10-07 10:13:00

50

Views

Does the mean of two positive numbers obey these basic inequalities?

Published on 07 Oct 2014 - 10:13

score 2.9k · Answer 14 · 2014-10-15 15:18:31

2.9k

Views

How to prove a finite field is not ordered?

Published on 15 Oct 2014 - 15:18

score 166 · Answer 15 · 2014-10-19 21:56:05

166

Views

Can an orderable field always be ordered in a way that extends a given subfield's ordering?

Published on 19 Oct 2014 - 21:56

List Question

Existence and uniqueness up to isomorphism of the real numbers from axioms

Ordered field with nested intervals axiom without Archimedean axiom

Proof that all ordered fields are in the Surreals

Are order isomorphic real closed fields isomorphic?

Replacing the "if $x ≤ y$, then $x + z ≤ y + z$" axiom in Reals.

In an Archimedian Field $F$, there is a positive rational element $r$ such that $r < z$ for any $ z>0$ in $F$

If $y,z$ are elements of an archimedean field $F$ and if $y<z$, then there is a rational element $r$ of $F$ such that $y<r<z$

Prove that if $F$ is an ordered field in which every non empty set which has an upper bound also has a supremum , then $F$ is archimedean

Is 1/2 less than 1?

Proving Properties in Ordered Fields

Is$\ +\infty$ greater than any other number (surreal, superreal, hyperreal, ...)?

How to prove: If $x \geq 0 $ and $x \leq \epsilon$, for all $\epsilon > 0$, then $x = 0$?

Does the mean of two positive numbers obey these basic inequalities?

How to prove a finite field is not ordered?

Can an orderable field always be ordered in a way that extends a given subfield's ordering?

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