May 2024
Intermediate to advanced
332 pages
15h 45m
English
Content preview from Discrete Mathematics
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28 DISCRETE MATHEMATIC..._
________________________
_
(c) QED
Cases
And the tricky case:
2.
If
z is defeated by someone then 3 a locally fair ranking
of
T with z frrst.
(a) Assume
z is defeated by someone.
(b) Choose
x to be someone who defeated
z.
(c) z has the best record in the subtournament involving all-but-x.
z had the best record in T, no wins are removed.
(d)
3 ranking
of
subtoumament having z frrst.
Inductive hypothesis,
z has the best record.
(e)
ChooseR
to
be
a ranking
of
all-but-x having z first.
(f)
In
T,
xis
defeated by someone.
z was defeated and
x's
record in T cannot
be
better than
z's.
(g) Define ranking
S to
be
R, with ...
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