The real numbers & completeness

What the problems look like

A few statements from this skill. Answers, hints and worked solutions live in the practice session.

1. Warm-up

   By the Archimedean property, the set of natural numbers $n$ satisfying $\dfrac{1}{n} < \dfrac{4}{15}$ is nonempty. Compute the least such natural number $n$.

2. Warm-up

   By the Archimedean property, the set of natural numbers $n$ satisfying $\dfrac{1}{n} < \dfrac{1}{14}$ is nonempty. Compute the least such natural number $n$.

3. Warm-up

   By the Archimedean property, the set of natural numbers $n$ satisfying $\dfrac{1}{n} < \dfrac{1}{19}$ is nonempty. Compute the least such natural number $n$.

Problems shown under their original terms: Generated (template, solver-computed).