query: Are the reals genuinely a subset of the complex numbers?
positive_passages.docid: 60775
positive_passages.text: Why are integers subset of reals?
negative_passages.docid: 30817
negative_passages.text: Is an automorphism of the field of real numbers the identity map?
negative_passages.docid: 41052
negative_passages.text: The set of real numbers and power set of the natural numbers
negative_passages.docid: 122181
negative_passages.text: Application of Complex Numbers
negative_passages.docid: 136287
negative_passages.text: Separate real and imaginary part of $\arccos(z)$
negative_passages.docid: 21769
negative_passages.text: Motivation for complex numbers
negative_passages.docid: 48028
negative_passages.text: True Definition of the Real Numbers
negative_passages.docid: 130297
negative_passages.text: $A$ be a subset of $[0,1]$ with non-empty interior ; then is it true that $\mathbb Q+A=\mathbb R$?
negative_passages.docid: 25788
negative_passages.text: Prove that $i^i$ is a real number
negative_passages.docid: 74024
negative_passages.text: Higher dimensional equivalent of complex numbers
negative_passages.docid: 66334
negative_passages.text: How is every subset of the set of reals with the finite complement topology compact?
negative_passages.docid: 84686
negative_passages.text: Geometric Description Of a Set In The Complex Plane
negative_passages.docid: 9969
negative_passages.text: Is infinity a real number?
negative_passages.docid: 73927
negative_passages.text: Is $\mathbb{R}$ a subset of $\mathbb{R}^2$?
negative_passages.docid: 92390
negative_passages.text: The meaning of notation $\subset\subset$ in complex analysis
negative_passages.docid: 38674
negative_passages.text: Do complex numbers really exist?
negative_passages.docid: 146560
negative_passages.text: Is there any uncountably infinite set that does not generate the reals?