query: Infinite cardinality $\aleph_2$
positive_passages.docid: 152518
positive_passages.text: Proof that the set of all possible curves is of cardinality $\aleph_2$?
negative_passages.docid: 140662
negative_passages.text: Powers of infinite cardinals in the generic extension
negative_passages.docid: 114262
negative_passages.text: Find the cardinality of the following set $S_n=\{(x,y)|x^2+y^2=n, \text{where }x,y,n \in \mathbb Z\text{ and }n\geq0 \}$
negative_passages.docid: 151355
negative_passages.text: Are cardinal numbers well defined? Or could we have something like $\aleph_{1/2}$?
negative_passages.docid: 139078
negative_passages.text: Infinite partition of $\mathbb N$ by infinite subsets
negative_passages.docid: 20085
negative_passages.text: What's the cardinality of all sequences with coefficients in an infinite set?
negative_passages.docid: 127233
negative_passages.text: Cardinality of order types in $\mathbb{N}$
negative_passages.docid: 58267
negative_passages.text: Godel's pairing function and proving c = c*c for aleph cardinals
negative_passages.docid: 83518
negative_passages.text: Proving Two sets have same cardinality
negative_passages.docid: 101669
negative_passages.text: Cardinality of the Set of all finite subset of $\mathbb{R}$
negative_passages.docid: 69838
negative_passages.text: Does a countably infinite power set exist?
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: 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: 48278
negative_passages.text: Inequality about infinite cardinals
negative_passages.docid: 79725
negative_passages.text: Fields of arbitrary cardinality
negative_passages.docid: 45216
negative_passages.text: Cardinality of $[0,1]$
negative_passages.docid: 119624
negative_passages.text: A Dedekind infinite set has a countably infinite proper subset