bluemsi/2nd
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

docs: finalized wiki integrity maintenance (v3.0 standard) - pruned 1400+ stubs and fixed 11k+ ghost links

Browse Source
This commit is contained in:
Antigravity Agent
2026-05-02 09:18:34 +09:00
parent c84dcb8371
commit 6445fcc05b
13150 changed files with 55394 additions and 100862 deletions
Download Patch File Download Diff File Expand all files Collapse all files
01_Archive/2026-04-20/Conway's On Numbers and Games.md
+3 -3
View File
@@ -1,4 +1,4 @@
[[Conway's On Numbers and Games]]
[[Conway's On Numbers and Games|Conway's On Numbers and Games]]
📌 Brief Summary
*On Numbers and Games* (ONAG), authored by John Horton Conway in 1976, is a foundational treatise in combinatorial game theory. It introduces the concept of "surreal numbers," an algebraically closed field that encompasses both the real numbers and infinitely large/infinitesimal quantities, constructed through a recursive process of defining numbers via sets of previously defined numbers.
@@ -9,8 +9,8 @@
* **The Role of Infinitesimals:** A significant contribution of ONAG is the formalization of infinitesimals within a rigorous, non-standard analytic context. By treating $\epsilon$ (an infinitesimal) and $\omega$ (an infinite ordinal) as algebraic entities that obey standard arithmetic laws, Conway provided a toolset for analyzing games that may last an infinite number of moves or possess "fuzzy" values (games that are neither greater than, less than, nor equal to zero).
🔗 Knowledge Connections
* Related Topics: [[Combinatorial Game Theory]], [[Surreal Numbers]], [[Transfinite Induction]], [[Non-standard Analysis]]
* Projects/Contexts: [[The construction of the field of Surreal Numbers]], [[Analysis of impartial and partizan games (e.g., Hackenbush, Go, Chess)]]
* Related Topics: [[Combinatorial Game Theory|Combinatorial Game Theory]], [[Surreal Numbers|Surreal Numbers]], Transfinite Induction, Non-standard Analysis
* Projects/Contexts: The construction of the field of Surreal Numbers, Analysis of impartial and partizan games (e.g., Hackenbush, Go, Chess)
* Contradictions/Notes: While ONAG provides the algebraic foundation for surreal numbers, modern computational implementations often use more efficient "dyadic" representations rather than the full set-theoretic construction to avoid the complexities of transfinite induction in finite memory.
Last updated: 2026-04-16