# Questions tagged [surreal-numbers]

For questions about the surreal numbers, which are a real-closed ordered proper-class-sized field that contains both the real numbers and the ordinal numbers. Thus they contain both infinite numbers (including the ordinals, but also infinite numbers like ω-1 and sqrt(ω)) and infinitesimal numbers (like 1/ω). They can also be identified with a subclass of two-player partisan games.

**5**

**1**answer

### Are the Surreals a cogenerator in the category of ordered fields?

**15**

**2**answers

### Is the surreal number $\omega(\sqrt{2}+1)+1$ a prime?

**0**

**0**answers

### Can one represent divergent integrals or germs at infinity with surreal numbers?

**2**

**0**answers

### Surreal numbers and the Collatz iteration as a game?

**5**

**0**answers

### Quantum surreal numbers

**2**

**1**answer

### Smallest ring whose field of fractions includes all the reals (subring of omnific integers?)

**7**

**0**answers

### How does Conway's proposed compromise for constructing the real numbers in ONAG actually work?

**15**

**1**answer

### In theory, how would Oneiric numbers be defined?

**24**

**1**answer

### Are Conway's combinatorial games the “monster model” of any familiar theory?

**0**

**0**answers

### Is standard, affine infinity of extended reals quite small on the scale of infinities?

**4**

**1**answer

### Surreal numbers and the Axiom of Choice

**36**

**3**answers

### Who discovered the surreals?

**16**

**2**answers

### Biggest Field Of Characteristic $p$

**5**

**0**answers

### Algebraic Geometry Over the Surreal and Surrcomplex Numbers

**5**

**0**answers

### The surreal numbers under a change of universe

**9**

**0**answers

### Genetic construction of roots of surreal polynomials

**3**

**1**answer

### 'Smallest' subfield of the Surreals which is isomorphic to the Surreals as an ordered group

**6**

**1**answer

### Surreal Numbers, Proving $x1=x$

**34**

**2**answers

### Who wins two player sudoku?

**2**

**1**answer

### Functions on a field representable by Hahn series?

**7**

**1**answer

### Is the inverse of surreal numbers actually well-defined?

**12**

**1**answer

### Largest ordered “field” in NBG without axiom of global choice

**4**

**1**answer

### Roots of $\omega$, larger $\gamma$-numbers

**6**

**2**answers

### Automorphism of the transfinite rooted binary tree

**4**

**0**answers

### Modern advances in combinatorial game theory

**10**

**2**answers

### What surreal numbers are representable by Red-Blue Hackenbush games?

**2**

**1**answer

### Are Surreal Numbers the same as Trans-series?

**5**

**1**answer

### Can a game be an option of itself?

**9**

**1**answer

### Surreal number: trying to construct complete ordered fields

**2**

**0**answers

### Factorization in the Omnific Integers

**3**

**1**answer

### Sign-expansion definition of Surreal arithmetical operations

**31**

**1**answer

### Are there any interesting surreal constants?

**14**

**1**answer

### The surreal version of $e$

**7**

**1**answer

### Going beyond the surreal numbers

**1**

**0**answers

### A question about real closed fields that contain the real numbers as a proper subfield

**1**

**0**answers

### A (second-order) axiomatic characterization of the integers which rules out surreal/hyperreal versions

**6**

**1**answer

### Is $\omega^\frac{1}{\omega} > n \forall n \in \mathbb{N}$?

**2**

**0**answers

### Extension to real number system [closed]

**18**

**0**answers

### Is the universality of the surreal number line a weak global choice principle?

**5**

**1**answer

### Ordinals which embed in surreal subfields

**9**

**2**answers

### Surreal compactness

**9**

**1**answer

### Pontryagin dual of the surreal numbers?

**18**

**2**answers

### Nice sign-expansions of special surreal numbers

**3**

**0**answers

### Nimbers and Surreal Numbers [closed]

**5**

**1**answer

### Is it possible to evaluate Connect 4 positions with Combinatorial Game Theory?

**11**

**3**answers

### First-order definable bijection between $P(On)$ (or $No$) and $V$? (Is this equivalent to $V = HOD$?)

**8**

**1**answer

### Transcendence degree of the surreals over the subfield generated by the ordinals

**10**

**3**answers

### Does this construction yield the surreal numbers?

**6**

**0**answers

### More information on Kruskal's treatment of Surreal numbers as an asymptotic behavior of a real valued function

**3**

**0**answers