Creating theorems from the given axioms

  • Context: MHB 
  • Thread starter Thread starter dezzi1
  • Start date Start date
  • Tags Tags
    Axioms
Click For Summary
SUMMARY

The discussion focuses on creating theorems based on four axioms related to game theory. The established axioms state that each game is played by two distinct teams, there are at least four teams, at least six games are played, and each team plays at most four games. Two theorems have been proposed: the existence of at least two teams that play a game and the condition that if there are exactly four teams, then there are at most eight games. The user seeks assistance in proving the second theorem and creating a third theorem.

PREREQUISITES
  • Understanding of basic game theory concepts
  • Familiarity with axiomatic systems
  • Knowledge of theorem proving techniques
  • Experience with logical reasoning and mathematical proofs
NEXT STEPS
  • Research methods for proving theorems in game theory
  • Study combinatorial game theory principles
  • Explore the concept of team combinations and game pairings
  • Learn about constructing additional theorems from axioms
USEFUL FOR

Mathematicians, game theorists, students studying logic and proofs, and anyone interested in developing and proving theorems based on axiomatic foundations.

dezzi1
Messages
1
Reaction score
0
Given the following axioms, create 3 theorems.

Axiom 1: Each game is played by two distinct teams.
Axiom 2: There are at least four teams.
Axiom 3: At least six games are played.
Axiom 4: Each team plays at most four games.

I have already proven each axioms independence.

These are the following theorems I have:
1. There are at least 2 teams that play a game
2. If there are exactly 4 teams then there at most 8 games

I have completely proven theorem 1. I just need help proving theorem 2 and creating/proving a third theorem.

Any help will be greatly appreciated!
 
Physics news on Phys.org
Hello and welcome to MHB, dezzi! :D

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?
 

Similar threads

MHB Proving Theorem 2: At Least 2 Games Played
  • · Replies 3 ·
Replies
3
Views
2K
MHB Creating theorems for an axiomatic system
  • · Replies 1 ·
Replies
1
Views
2K
MHB Proving Independence of Axioms in Game Theory: A Case Study
  • · Replies 5 ·
Replies
5
Views
4K
MHB Axioms of Set Theory: Separation Axiom and Garling Theorem 1.2.2 .... ....
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Set Theory: Separation Axiom and Garling's Theorem 1.2.2
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Is an algorithm for a proof required to halt?
  • · Replies 3 ·
Replies
3
Views
2K
High School Is everything in math either an axiom or a theorem?
  • · Replies 72 ·
3
Replies
72
Views
8K
MHB Axioms of Set Theory .... and the Union of Two Sets ....
  • · Replies 2 ·
Replies
2
Views
2K
MHB Coming up with Theorems and proving them
  • · Replies 7 ·
Replies
7
Views
11K
Undergrad Solving Hangman's Paradox: Axioms, Deductions & Probabilities
  • · Replies 10 ·
Replies
10
Views
2K