query: Proving the real numbers are complete
positive_passages.docid: 4552
positive_passages.text: Choice of $q$ in Baby Rudin's Example 1.1
negative_passages.docid: 30478
negative_passages.text: How to prove that a number is irrational
negative_passages.docid: 13273
negative_passages.text: Cardinality of the set of all real functions of real variable
negative_passages.docid: 137718
negative_passages.text: Prove that the complex expression is real
negative_passages.docid: 75625
negative_passages.text: Complete residue system proof
negative_passages.docid: 99656
negative_passages.text: Prove that the set of all algebraic numbers is countable
negative_passages.docid: 41052
negative_passages.text: The set of real numbers and power set of the natural numbers
negative_passages.docid: 81154
negative_passages.text: Characterising reals with terminating decimal expansions
negative_passages.docid: 52380
negative_passages.text: How to prove the function $e^x$ is continous for all real numbers
negative_passages.docid: 55119
negative_passages.text: Proof that the coefficients of a polynomial are real
negative_passages.docid: 33998
negative_passages.text: Show that given seven real numbers, it is always possible take two of them, such that $\left\vert\frac{a-b}{1+ab}\right\vert<\frac{1}{\sqrt{3}}$
negative_passages.docid: 70196
negative_passages.text: Is there any well-ordered uncountable set of real numbers under the original ordering?
negative_passages.docid: 1396
negative_passages.text: cardinality of all real sequences
negative_passages.docid: 2269
negative_passages.text: Proof that the real numbers are countable: Help with why this is wrong
negative_passages.docid: 88887
negative_passages.text: Using the properties of real numbers, verify commutativity on complex numbers.
negative_passages.docid: 31900
negative_passages.text: Induction on Real Numbers
negative_passages.docid: 152976
negative_passages.text: Real Analysis: open and closed sets