 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-oxford/2017/prelims/mathematics-ii/1/b/ii/solution

True. Set

l = in f A

and

v = in f {in f R_{m} : m \geq 1}

. Because

R_{m} \subseteq A

, every row infimum satisfies

in f R_{m} \geq l

, so

v \geq l

. But

x_{m, n} \geq in f R_{m} \geq v

for all

m, n

, making

v

A

. Therefore

v \leq l

, and

in f A = m \geq 1 in f n \geq 1 in f x_{m, n} .

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