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Putnam
1959 Putnam
A4
A4
Part of
1959 Putnam
Problems
(1)
Putnam 1959 A4
Source: Putnam 1959
6/15/2022
If
f
f
f
and
g
g
g
are real-valued functions of one real variable, show that there exist
x
x
x
and
y
y
y
in
[
0
,
1
]
[0,1]
[
0
,
1
]
such that
∣
x
y
−
f
(
x
)
−
g
(
y
)
∣
≥
1
4
.
|xy-f(x)-g(y)|\geq \frac{1}{4}.
∣
x
y
−
f
(
x
)
−
g
(
y
)
∣
≥
4
1
.
Putnam
function
real analysis