query: Why is Cantor's diagonal argument valid?
positive_passages.docid: 6681
positive_passages.text: How does Cantor's diagonal argument work?
negative_passages.docid: 63952
negative_passages.text: Disproving: If $(\Gamma\vdash(\phi\,\lor\psi))$, either $(\Gamma\vdash\phi)$ or $(\Gamma\vdash\psi)$ is true
negative_passages.docid: 73415
negative_passages.text: The reason why the existence of inaccessible cardinals cannot be proven in ZFC
negative_passages.docid: 84378
negative_passages.text: Does axiom of foundation/regularity protect against Russell-like paradoxes?
negative_passages.docid: 86926
negative_passages.text: Why isn't this a well ordering of $\{A\subseteq\mathbb N\mid A\text{ is infinite}\}$?
negative_passages.docid: 48727
negative_passages.text: Why is the Cantor set not defined by a limit?
negative_passages.docid: 47653
negative_passages.text: Cantor diagonalization and fundamental theorem
negative_passages.docid: 147350
negative_passages.text: Homeomorphism between $\prod X_i$ and the Cantor set
negative_passages.docid: 109054
negative_passages.text: Given an infinite set of cardinality $X$, is there a chain in $\mathcal P(X)$ of the same cardinalty of $\mathcal P(X)$?
negative_passages.docid: 2269
negative_passages.text: Proof that the real numbers are countable: Help with why this is wrong
negative_passages.docid: 272
negative_passages.text: Cantor Sets/nonempty/cardinality
negative_passages.docid: 20706
negative_passages.text: Non-existence of a Surjective Function from a Set to Its Subsets (Cantor's theorem)
negative_passages.docid: 43462
negative_passages.text: Disprove $\mathcal{P}(A\Delta B) \setminus \{\emptyset\} = \mathcal{P}(A) \Delta\mathcal{P}(B) $. Is my proof good?
negative_passages.docid: 154240
negative_passages.text: Inverse of Heine–Cantor theorem
negative_passages.docid: 22408
negative_passages.text: Jutifying: irrational + rational = irrational
negative_passages.docid: 1027
negative_passages.text: Why is this true? $(\exists x)(P(x) \Rightarrow (\forall y) P(y))$
negative_passages.docid: 108922
negative_passages.text: Cardinality and infinite sets: naturals, integers, rationals, bijections