All Questions
Tagged with combinatorial-game-theory surreal-numbers
14 questions
8
votes
1
answer
580
views
Birthday of combinatorial game product
Recall that the birthday $B(G)$ of a combinatorial game $G$ is recursively defined as the least ordinal $\alpha$ such that $G = \{L | R\}$ for some sets of games $L$, $R$ with birthdays less than $\...
- 447
1
vote
0
answers
132
views
Are gaps and loopy games interchangeable in the Surreal Numbers?
The class of surreal numbers (commonly called $No$) is not complete: it contains gaps. Some people have studied the "Dedekind completion" of the surreal numbers in order to do limits and ...
3
votes
1
answer
329
views
What does it mean for the surreal numbers/partizan games to be "universally embedding"?
In "On numbers and games", Conway writes that the surreal Numbers form a universally embedding totally ordered Field. Later Jacob Lurie proved that (the equivalence classes of) the partizan ...
- 83
7
votes
0
answers
285
views
Quantum surreal numbers
Toward Quantum Combinatorial Games presents the definition of a "quantum game", allowing a superposition of moves rather than a single classical move. This leaves me wondering: Since surreal ...
- 171
8
votes
0
answers
327
views
How does Conway's proposed compromise for constructing the real numbers in ONAG actually work?
I have also asked this question on Math Stack Exchange (link).
In On Numbers and Games, after discussing the inclusion of the real numbers in the surreal numbers, No, Conway discusses the merits of ...
- 455
16
votes
1
answer
2k
views
In theory, how would Oneiric numbers be defined?
Background I am not a professional mathematician. I am researching Surreal numbers & games for fun (I think they are truly beautiful). If this question is not appropriate here, I beg forgiveness &...
- 169
27
votes
1
answer
2k
views
Are Conway's combinatorial games the "monster model" of any familiar theory?
This is related to this question about a "mother of all" groups, and so seemed like it'd fit in better at MO than MSE.
If I understand the answer to that question correctly, the surreal numbers have ...
- 4,907
35
votes
2
answers
5k
views
Who wins two player sudoku?
Let's say players take turns placing numbers 1-9 on a sudoku board. They must not create an invalid position (meaning that you can not have the same number in within a row, column, or box region). The ...
- 6,403
5
votes
0
answers
184
views
Modern advances in combinatorial game theory
I'm going to take part in teaching a course in combinatorial game theory in the best of ONAG's spirit. I was wondering if there are interesting post-ONAG results that are worth mentioning in (a later ...
- 5,590
10
votes
2
answers
1k
views
What surreal numbers are representable by Red-Blue Hackenbush games?
Every game of Red-Blue Hackenbush represents a surreal number. Is the converse true? Assuming that it is false, what can be said about the class of surreal numbers that are representable by such ...
- 203
3
votes
1
answer
462
views
Are Surreal Numbers the same as Trans-series?
I recently found the paper of Berarducci + Mantova [1, 2] saying that surreal numbers are equivalent to trans-series. These are very different objects:
trans-series are used in physics to correct, ...
- 22.8k
5
votes
1
answer
459
views
Can a game be an option of itself?
My question is, can a game contain itself as an option? and can it be a surreal number? For example $A=\{A|\}$ or $B=\{C|B\}$ where $C$ is a surreal number.
from the point of view of games, it is ...
- 51
3
votes
0
answers
715
views
Nimbers and Surreal Numbers [closed]
I have been researching Combinatorial Game Theory. One common theme is the assignment of values to games in order to classify the game as a win for a specific player. One such way is class of surreal ...
- 1,129
6
votes
1
answer
2k
views
Is it possible to evaluate Connect 4 positions with Combinatorial Game Theory?
The surreal numbers in Combinatorial Game Theory only work for certain classes of games (e.g. they must satisfy normal play convention). This rules out even reasonable games with fairly well-...
- 22.8k