[BLML] Cheshire cat [SEC=UNOFFICIAL]
blml at arcor.de
Fri Sep 10 10:49:19 CEST 2010
Alain Gottcheiner <agot at ulb.ac.be> wrote:
> Le 9/09/2010 19:49, Jean-Pierre Rocafort a écrit :
> >> Most relations of the "competition" type (those which represent results
> >> of a round-robin without draws) are (at least theoretically)
> >> non-transitive.
> >> And that's why I claimed that the two counterexamples were non-stone,
> >> i.e. "competition" rather than "better"
> >> In fact, the non-transitive set of dice invented by the late Martin
> >> Gardner serve to illustrate that there is a difference between those two
> >> types..
> >> In mathematics, "better" does not mean "being able to beat".
> >> There is an interesting theorem, that I see with my students : a
> >> "competition" relation is transitive if and only if there are no two
> >> competitors who have won the same number of matches.
> > i am not certain to understand what you mean. is it that you try a
> > posteriori to infer from the semi-random results of a round-robin
> > whether there is a relation of total order between contestants?
> > in what category do you range this competition (table-tennis team
> > competition used a few years ago):
> > a team is constituted of 3 players. in a match between 2 teams, each
> > player in a team meets the 3 players of the opposite team.
> > suppose there is a reliable ranking of 9 players (a player always wins
> > against a lower-ranking opponent).
> > team A consists of players 1, 5 and 9
> > team B: 2,6,7
> > team C: 3,4,8
> > A is better than B (it beats it 5-4)
> > B is better than C
> > C is better than A
> > we have the same phenomenon in bridge with suit combinations as jeroen
> > warmerdam showed: for instance with A1098 R432, there are 4 lines of
> > play A,B,C,D such as A is better than B (at BAM scoring), B than C, C
> > than D and D than A.
> I would like to add something about the "nothing is better than Love"
> Yesterday evening, I was in very international company, so i conducted a
> poll. It appeared that only English (and perhaps Japanese) does have an
> ambiguity problem with this sentence.
The ambiguity is exactly the same in German.
A few other similar ambiguity also are identical in English
and in German, such as "They want only our best, but they won't get it".
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