User:IssaRice/Increasingly granular measuring stick

Exercise 3.6.6 in Rosenthal's A First Look at Rigorous Probability Theory.

Theorem 5.5.9 (existence of least upper bound) and Proposition 5.4.14/exercise 5.4.5 in Tao's Analysis I.

I think all of these can be visualized as a "measuring stick" (on the real line) that gets progressively finer.