# 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.

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

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

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

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

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

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### Characteristic $p$ surreals for $p \ne 2$? [duplicate]

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### Surreal numbers and the Axiom of Choice

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### Who discovered the surreals?

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### Biggest Field Of Characteristic $p$

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### Algebraic Geometry Over the Surreal and Surrcomplex Numbers

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### The surreal numbers under a change of universe

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### Genetic construction of roots of surreal polynomials

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

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

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### Who wins two player sudoku?

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

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

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

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

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### Automorphism of the transfinite rooted binary tree

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### Modern advances in combinatorial game theory

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

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

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

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

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### Factorization in the Omnific Integers

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### Sign-expansion definition of Surreal arithmetical operations

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### Are there any interesting surreal constants?

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### The surreal version of $e$

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### Going beyond the surreal numbers

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

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

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

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### Extension to real number system [closed]

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

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### Ordinals which embed in surreal subfields

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### Surreal compactness

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### Pontryagin dual of the surreal numbers?

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### Nice sign-expansions of special surreal numbers

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### Nimbers and Surreal Numbers [closed]

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

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

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

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### Does this construction yield the surreal numbers?

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

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### An application of surreal numbers towards fast-growing ordinal functors?

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### Surreal numbers, ultrapowers of $\Bbb R$, ordinal-valued functions and the slow-growing hierarchy

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### Is a certain group, derivable from the surreal numbers, isomorphic to the surreal numbers?

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### Is it possible to generalize functions like $x^y, \ln x, \sin x, \arctan x$ to surreal numbers or surcomplex numbers?

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