query: Cardinal arithmetic. Does hold $A>B\Rightarrow 2^A>2^B$?
positive_passages.docid: 140531
positive_passages.text: Why continuum function isn't strictly increasing?
negative_passages.docid: 67483
negative_passages.text: Show that $|a-b|<\epsilon \Rightarrow |a|<|b|+\epsilon$
negative_passages.docid: 142267
negative_passages.text: If two sets have the same cardinality, then so do their power sets. Converse can't be answered?
negative_passages.docid: 93330
negative_passages.text: Cardinality of all cardinalities
negative_passages.docid: 117047
negative_passages.text: exponentiation of cardinal number
negative_passages.docid: 5639
negative_passages.text: No \xrightrightarrow[a]{b}?
negative_passages.docid: 151355
negative_passages.text: Are cardinal numbers well defined? Or could we have something like $\aleph_{1/2}$?
negative_passages.docid: 46613
negative_passages.text: What's the difference between $\equiv$ and $\leftrightarrow$ in a formal proof?
negative_passages.docid: 48523
negative_passages.text: Let $A$ be any uncountable set, and let $B$ be a countable subset of $A$. Prove that the cardinality of $A = A - B $
negative_passages.docid: 136835
negative_passages.text: ZF Set Theory - If $|A|^{|B|} = |B|$, then $|A| = 1 = |B|.$
negative_passages.docid: 131844
negative_passages.text: When does $(e^a)^b = e^{ab}$ hold?
negative_passages.docid: 38764
negative_passages.text: bound on the cardinality of the continuum? I hope not
negative_passages.docid: 31173
negative_passages.text: How to show $(a^b)^c=a^{bc}$ for arbitrary cardinal numbers?
negative_passages.docid: 139503
negative_passages.text: How to prove $|a+b|^k \leq 2^{k-1} (|a|^k+|b|^k)$?
negative_passages.docid: 52880
negative_passages.text: Intuition: If $a\leq b+\epsilon$ for all $\epsilon>0$ then $a\leq b$?
negative_passages.docid: 35043
negative_passages.text: Cardinality of a set A is strictly less than the cardinality of the power set of A
negative_passages.docid: 111720
negative_passages.text: Is "have the same cardinality" a equivalence relation?