Challenge questions from FPM quizzes: First quiz on rational and irrational numbers

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 My second FPM quiz last autumn was a First quiz on rational and irrational numbers.

Here is a screenshot of the challenge question.

Note added: Thanks for asking about whether zero is a natural number. This varies in the literature, and (as you can check) the answer here depends crucially on this. For my teaching in Nottingham, zero is not included in the natural numbers. So the natural numbers are the strictly positive integers, i.e.,

\[\mathbb{N}=\{1,2,3,\dots\}\,.\]
Quiz question


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