query: How to show the cardinality $0$ is less than the cardinality $1$
positive_passages.docid: 145574
positive_passages.text: Empty function, what is it?
negative_passages.docid: 73850
negative_passages.text: Cardinality of set of functions
negative_passages.docid: 144787
negative_passages.text: Show that the set of all infinite subsets of $\mathbb{N}$ has cardinality greater than $\mathbb{N}$
negative_passages.docid: 65768
negative_passages.text: What is the cardinality of the set of the empty set?
negative_passages.docid: 117047
negative_passages.text: exponentiation of cardinal number
negative_passages.docid: 142631
negative_passages.text: Show that A has the same cardinality as $A\setminus\{x,y,z\}$
negative_passages.docid: 78300
negative_passages.text: Showing a set is closed other than giving a counterexample?
negative_passages.docid: 74281
negative_passages.text: Proof there is no largest cardinal number
negative_passages.docid: 111954
negative_passages.text: Computing the cardinality of a combinatorial set
negative_passages.docid: 98163
negative_passages.text: Question regarding exponentiation of cardinal numbers
negative_passages.docid: 106585
negative_passages.text: Show $d_{1}(x_{n},x)\rightarrow{0}$ if and only if $d_{2}(x_{n},x)\rightarrow{0}$.
negative_passages.docid: 116501
negative_passages.text: How to show equinumerosity of  the powerset of $A$ and the set of functions from $A$ to $\{0,1\}$ without cardinal arithmetic?
negative_passages.docid: 93606
negative_passages.text: Showing that $C[0,1]$ is not complete
negative_passages.docid: 38764
negative_passages.text: bound on the cardinality of the continuum? I hope not
negative_passages.docid: 49440
negative_passages.text: Prove that the interval $ \ [0,2)$ and $ \ [5,6) \cup [7,8)$ have the same cardinality
negative_passages.docid: 127233
negative_passages.text: Cardinality of order types in $\mathbb{N}$
negative_passages.docid: 132382
negative_passages.text: Showing a set is nowhere dense in $C([0,1])$