By Dedekind's cut we can define some irrational number, where L and R are two disjoint sets of all rational numbers.(adsbygoogle = window.adsbygoogle || []).push({});

We know that rational and irrational numbers have different properties, that give us the ability to clearly distinguish between a rational number (expressed as a ratio between at least two integers) and an irrational numbers (cannot be expressed as a ratio between at least two integers).

My question is this:

Since rational and irrational numbers are clearly distinguished from each other, then what is the purpose of Dedekind’s cut, and why the word ‘cut’ is used here?

Thank you.

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# A Dedekind's cut question

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