MHB Creating theorems for an axiomatic system

  • Thread starter Thread starter malloryjohn
  • Start date Start date
  • Tags Tags
    System
Click For Summary
The discussion centers on formulating theorems based on a defined set of axioms regarding team games. The established theorem states that with exactly four teams, there can be at most eight games. Participants are encouraged to explore additional theorems by fixing one variable and analyzing the implications for the others. Key questions include determining the maximum number of teams possible with exactly six games played and the scenario where each team plays only once. The conversation emphasizes the importance of understanding the relationships between the number of teams, games, and game participation limits.
malloryjohn
Messages
1
Reaction score
0
I have the axioms:

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

And I have come up with the theorem: If there are exactly 4 teams, then there are at most 8 games.

I need to come up with two more theorems. I'm pretty stuck on where to go from here, so any advice would be greatly appreciate
 
Physics news on Phys.org
How many teams can there be, if there are exactly six games played?

If each team plays only once, how many teams can there be (if only teams that play games count)?

The general idea is: fix ONE of your variables, and determine limits on the others.
 

Thread 'How do E[X] and E[|X|] relate?'

Greetings, I am studying probability theory [non-measure theory] from a textbook. I stumbled to the topic stating that Cauchy Distribution has no moments. It was not proved, and I tried working it via direct calculation of the improper integral of E[X^n] for the case n=1. Anyhow, I wanted to generalize this without success. I stumbled upon this thread here: https://www.physicsforums.com/threads/how-to-prove-the-cauchy-distribution-has-no-moments.992416/ I really enjoyed the proof...
View full post »

Similar threads

MHB Creating theorems from the given axioms
  • · Replies 1 ·
Replies
1
Views
1K
MHB Proving Theorem 2: At Least 2 Games Played
  • · Replies 3 ·
Replies
3
Views
2K
MHB Proving Independence of Axioms in Game Theory: A Case Study
  • · Replies 5 ·
Replies
5
Views
4K
MHB Coming up with Theorems and proving them
  • · Replies 7 ·
Replies
7
Views
11K
Graduate Formal axiom systems and the finite/infinite sets
  • · Replies 10 ·
Replies
10
Views
2K
MHB Game Night : Number of combinations
  • · Replies 14 ·
Replies
14
Views
2K
You sports people: methods for qualifying (for darts, in this case)
  • · Replies 12 ·
Replies
12
Views
2K
High School Validating Darts Tournament Skill Levels: A Non-Intrusive Approach
  • · Replies 4 ·
Replies
4
Views
2K
High School Baccarat math and beating the edge
  • · Replies 1 ·
Replies
1
Views
2K
Is mathematics invented or discovered?
  • · Replies 2 ·
Replies
2
Views
423