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Tann
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By Dedekind's cut we can define some irrational number, where L and R are two disjoint sets of all rational numbers.
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.
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.