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International Contests
IMO Shortlist
1969 IMO Shortlist
59
59
Part of
1969 IMO Shortlist
Problems
(1)
Construct a continuous function satisfying conditions
Source:
10/4/2010
(
S
W
E
2
)
(SWE 2)
(
S
W
E
2
)
For each
λ
(
0
<
λ
<
1
\lambda (0 < \lambda < 1
λ
(
0
<
λ
<
1
and
λ
=
1
n
\lambda = \frac{1}{n}
λ
=
n
1
for all
n
=
1
,
2
,
3
,
⋯
)
n = 1, 2, 3, \cdots)
n
=
1
,
2
,
3
,
⋯
)
, construct a continuous function
f
f
f
such that there do not exist
x
,
y
x, y
x
,
y
with
0
<
λ
<
y
=
x
+
λ
≤
1
0 < \lambda < y = x + \lambda \le 1
0
<
λ
<
y
=
x
+
λ
≤
1
for which
f
(
x
)
=
f
(
y
)
.
f(x) = f(y).
f
(
x
)
=
f
(
y
)
.
function
algebra
continuous function
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