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So far what I know about Dedekind cuts are 1. it contains a rational number but does not contain all rational numbers 2. every rational number in the set is smaller than every rational number not belonging to the set. 3. it does not contain a greatest rational number

Joesixpack
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  • This request seems too broad. – anon Oct 30 '19 at 01:48
  • what do you mean? – Joesixpack Oct 30 '19 at 01:54
  • The usual identification is that a Dedekind cut is exactly the set of rational numbers strictly less than a specific real number $r$. This is how you use the rationals to construct the reals. A real number is a Dedekind cut, and the real numbers are ordered by set inclusion. – Robert Shore Oct 30 '19 at 01:54
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    It sounds like you have a fine definition of Dedekind Cut. Can you clarify what proofs you want to write that you need to know more for? For instance, if you want definitions of an order or of operations on Dedekind Cuts, you can find them on Wikipedia, in a textbook, or some other resource online. If you have no experience writing math proofs at all, that's a different question entirely. – Mark S. Oct 30 '19 at 09:09

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