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existence of surjections

Source: LIMIT 2019 CCS1 P2

April 28, 2021
function

Problem Statement

Which of the following are true? <spanclass=′latex−bold′>(A)</span> ∃f:N→Z onto and increasing<span class='latex-bold'>(A)</span>~\exists f:\mathbb N\to\mathbb Z\text{ onto and increasing} <spanclass=′latex−bold′>(B)</span> ∃f:Z→Q onto and increasing<span class='latex-bold'>(B)</span>~\exists f:\mathbb Z\to\mathbb Q\text{ onto and increasing} <spanclass=′latex−bold′>(C)</span> ∃f:Q→Z onto and increasing and bounded<span class='latex-bold'>(C)</span>~\exists f:\mathbb Q\to\mathbb Z\text{ onto and increasing and bounded} <spanclass=′latex−bold′>(D)</span> None of the above<span class='latex-bold'>(D)</span>~\text{None of the above}
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