query: Integers, rationals and reals as sets?
positive_passages.docid: 22498
positive_passages.text: In set theory, how are real numbers represented as sets?
negative_passages.docid: 152976
negative_passages.text: Real Analysis: open and closed sets
negative_passages.docid: 68976
negative_passages.text: Given real numbers: define integers?
negative_passages.docid: 30519
negative_passages.text: "Real" cardinality, say, $\aleph_\pi$?
negative_passages.docid: 22232
negative_passages.text: Proving that cardinality of the reals = cardinality of $[0,1]$
negative_passages.docid: 120935
negative_passages.text: Why is every continuous function on the reals determined by its value on rationals?
negative_passages.docid: 11405
negative_passages.text: If a nonempty set of real numbers is open and closed, is it $\mathbb{R}$? Why/Why not?
negative_passages.docid: 73927
negative_passages.text: Is $\mathbb{R}$ a subset of $\mathbb{R}^2$?
negative_passages.docid: 10472
negative_passages.text: Is every set a subset?
negative_passages.docid: 132525
negative_passages.text: Real Numbers Raised to Imaginary Powers?
negative_passages.docid: 62792
negative_passages.text: Can sum of a rational number and its reciprocal be an integer?
negative_passages.docid: 19138
negative_passages.text: If every object in math can be reduced to sets, how are tuples explained via sets?
negative_passages.docid: 98577
negative_passages.text: Show that the set $\mathbb{Q}(\sqrt{p})=\{a+b\sqrt{p}; a,b,p\in\mathbb{Q},\sqrt{p}\notin \mathbb{Q}\}$ is a field
negative_passages.docid: 70196
negative_passages.text: Is there any well-ordered uncountable set of real numbers under the original ordering?
negative_passages.docid: 32441
negative_passages.text: How to prove or disprove statements about sets
negative_passages.docid: 324
negative_passages.text: Show uncountable set of real numbers has a point of accumulation
negative_passages.docid: 58636
negative_passages.text: Do the real numbers and the complex numbers have the same cardinality?