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.
Questions tagged [surreal-numbers]
78 questions
10
votes
1 answer
In surreal numbers, what is $\ln \omega$?
Can this number $\ln \omega$ be written in $\{L|R\}$ form? What's its birthday?
Anixx
- 9,302
9
votes
3 answers
Uniformizing the surcomplex unit circle
Is the multiplicative Group of surcomplex numbers of modulus 1 isomorphic to the additive Group of the surreal numbers modulo the sub-Group of surreal integers? And, do Norman Alling's surreal extensions of sine and cosine (defined in section 7.5…
James Propp
- 19,363
6
votes
1 answer
Surreal Numbers, Proving $x1=x$
I am trying to learn the theory of the Surreal numbers and I am therefore going over all the theorems and trying to prove them for myself.
I am struggling to complete the proof of $x1 = x$.
I have the following. Assume x is a surreal number.
Then…
Nikolai Opdan
- 123
4
votes
1 answer
Roots of $\omega$, larger $\gamma$-numbers
In Harry Gonshor's An Introduction to the Theory of Surreal Numbers, on page 50, Gonshor points to a method for intuitively guessing what the square root of the countable infinity is in his construction -- I have a generalization of this intuitive…
Alec Rhea
- 9,009
4
votes
1 answer
Sign-expansion definition of Surreal arithmetical operations
Is there a way to define the addition and multiplication operations in Surreals numbers, defined directly on the sign-expansion notation {-,+}, i.e. without firstly convert them to the Conway notation {L|R}?
Dr.Zoidberg
- 41
3
votes
0 answers
An application of surreal numbers towards fast-growing ordinal functors?
The surreal numbers $\mathbb{SN}$ form a class of numbers introduced by J.H. Conway, which behave as an ordered field (even if technically it is not a set). In particular, Conway showed that every ordered field can be embedded by $\mathbb{SN}$ as it…
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