I'm trying to wrap my head around these Dedekind cuts. The definition is straightforward but I'm a little confused about the downward closure part.(adsbygoogle = window.adsbygoogle || []).push({});

##x \in Q## and ##y<x \Longrightarrow y \in Q##

Does that mean that this is not a cut because it is bounded below?

{## x \in Q : x>1 \wedge x<2 ##}

Clear this up for me please.

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# I Dedekind Cuts

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