Question 27
The closed interval $A = [0, 50]$ is the union of a finite number of closed intervals, each of length $1$. Prove that some of the intervals can be removed so that those remaining are mutually disjoint and have total length $\geq 25$.
Note. For $a \leq b$, the closed interval $[a, b] := \{ x \in \mathbb{R} : a \leq x \leq b \}$ has length $b - a$; disjoint intervals have empty intersection.
Note. For $a \leq b$, the closed interval $[a, b] := \{ x \in \mathbb{R} : a \leq x \leq b \}$ has length $b - a$; disjoint intervals have empty intersection.