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16 votes

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More than the real numbers: hyperreals, superreals, surreals ...?

answered Oct 8, 2015 at 15:38

14 votes

Why can mathematical induction only be used with natural numbers?

answered Jul 28, 2015 at 20:35

10 votes

Showing that minimal polynomial has the same irreducible factors as characteristic polynomial

answered Apr 22, 2018 at 23:05

10 votes

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Surcomplex numbers and the largest algebraically closed field

answered Jan 26, 2017 at 23:09

7 votes

Examples of Surreal Numbers that are only Surreal Numbers?

answered Apr 22, 2018 at 16:19

7 votes

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Does every total order embed into the surreal numbers?

answered Apr 28, 2020 at 10:32

6 votes

Is $\mathbb{N}$ definable over $(\mathbb{R},<,+,\cdot,0,1)$

answered May 2, 2016 at 14:30

6 votes

Dedekind completion of ordered fields

answered Nov 13, 2016 at 1:31

5 votes

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Are the hyperreals emerging at some stage of the surreal construction?

answered May 22, 2017 at 17:17

5 votes

What are some counter-intuitive results in mathematics that involve only finite objects?

answered Dec 4, 2016 at 10:27

5 votes

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Does surreal numbers with bounded birthdays form a field?

answered Feb 10, 2022 at 14:07

4 votes

Related to "division with remainder property"

answered Dec 27, 2017 at 22:15

4 votes

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Real Closed Fields with Predicate for a Dense Subfield

answered Jul 26, 2015 at 22:23

4 votes

In the surreal numbers, is it fair to say $0.9$ repeating is not equal to $1$?

answered Sep 20, 2015 at 19:24

4 votes

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Tarski-like axiomatization of spherical or elliptic geometry

answered Oct 13, 2015 at 9:26

4 votes

Is $\infty=\sqrt[\Omega]{\omega}$ actually a thing?

answered May 24, 2020 at 20:58

4 votes

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Formal Power Series as Initial Objects?

answered Jan 7, 2020 at 10:14

4 votes

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Surreal numbers and function growth

answered Nov 19, 2019 at 10:41

4 votes

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Seeking references on ordered fields

answered Dec 16, 2018 at 22:04

4 votes

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In Non-standard analysis, is the number of natural numbers a hyperreal number?

answered Apr 26, 2019 at 12:43

4 votes

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Juggling three non-Archimedean fields

answered Aug 8, 2018 at 23:10

4 votes

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Conway Notation for Large Countable Ordinals

answered Nov 22, 2018 at 9:18

4 votes

Can the field of Laurent series be made into an Archimedean ordered field?

answered Jan 18, 2022 at 16:31

3 votes

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Is the residue field of an algebraically closed valued field algebraically closed?

answered Oct 15, 2018 at 20:10

3 votes

What are superreal numbers?

answered May 3, 2018 at 10:08

3 votes

Any references on supercomplex/surcomplex numbers?

answered Dec 23, 2017 at 20:48

3 votes

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Completeness in Levi-Civita field

answered Mar 28, 2018 at 13:41

3 votes

"Lifting" an algebraic structure on a codomain to the set of functions into it.

answered Feb 24, 2019 at 14:21

3 votes

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

answered Aug 12, 2019 at 9:03

3 votes

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Find a transfinite monotone subsequence.

answered Sep 19, 2019 at 14:08

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145 Answers

More than the real numbers: hyperreals, superreals, surreals ...?

Why can mathematical induction only be used with natural numbers?

Showing that minimal polynomial has the same irreducible factors as characteristic polynomial

Surcomplex numbers and the largest algebraically closed field

Examples of Surreal Numbers that are only Surreal Numbers?

Does every total order embed into the surreal numbers?

Is $\mathbb{N}$ definable over $(\mathbb{R},<,+,\cdot,0,1)$

Dedekind completion of ordered fields

Are the hyperreals emerging at some stage of the surreal construction?

What are some counter-intuitive results in mathematics that involve only finite objects?

Does surreal numbers with bounded birthdays form a field?

Related to "division with remainder property"

Real Closed Fields with Predicate for a Dense Subfield

In the surreal numbers, is it fair to say $0.9$ repeating is not equal to $1$?

Tarski-like axiomatization of spherical or elliptic geometry

Is $\infty=\sqrt[\Omega]{\omega}$ actually a thing?

Formal Power Series as Initial Objects?

Surreal numbers and function growth

Seeking references on ordered fields

In Non-standard analysis, is the number of natural numbers a hyperreal number?

Juggling three non-Archimedean fields

Conway Notation for Large Countable Ordinals

Can the field of Laurent series be made into an Archimedean ordered field?

Is the residue field of an algebraically closed valued field algebraically closed?

What are superreal numbers?

Any references on supercomplex/surcomplex numbers?

Completeness in Levi-Civita field

"Lifting" an algebraic structure on a codomain to the set of functions into it.

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

Find a transfinite monotone subsequence.