Theorem: The rational line is not complete.

Proof: By contradiction. Assume the rational line is complete.
Then there exists a counterexample. Let A={x| and <2}. a<2. So 2 is a upper bound of A. Now we need to show that A doesn’t have a least upper bound.
<img src="/img/ratisincmplt.jpg"></img>
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Supplementary Materials

https://home.iitk.ac.in/~psraj/mth101/lecture_notes/lecture1.pdf