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Putnam
2001 Putnam
4
Putnam 2001 B4
Putnam 2001 B4
Source:
February 27, 2012
Putnam
college contests
Problem Statement
Let
S
S
S
denote the set of rational numbers different from
{
−
1
,
0
,
1
}
\{ -1, 0, 1 \}
{
−
1
,
0
,
1
}
. Define
f
:
S
→
S
f: S \rightarrow S
f
:
S
→
S
by
f
(
x
)
=
x
−
1
/
x
f(x)=x-1/x
f
(
x
)
=
x
−
1/
x
. Prove or disprove that
∩
n
=
1
∞
f
(
n
)
(
S
)
=
∅
\cap_{n=1}^{\infty} f^{(n)} (S) = \emptyset
∩
n
=
1
∞
f
(
n
)
(
S
)
=
∅
where
f
(
n
)
f^{(n)}
f
(
n
)
denotes
f
f
f
composed with itself
n
n
n
times.
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