query: Does taking power sets conserve inequality?
positive_passages.docid: 142267
positive_passages.text: If two sets have the same cardinality, then so do their power sets. Converse can't be answered?
negative_passages.docid: 33543
negative_passages.text: is "y1 < x < y2" an inequality or inequalities?
negative_passages.docid: 27587
negative_passages.text: inequality on the unit disk
negative_passages.docid: 9082
negative_passages.text: Do sets, whose power sets have the same cardinality, have the same cardinality?
negative_passages.docid: 138279
negative_passages.text: Multiplicative order and powers
negative_passages.docid: 24617
negative_passages.text: Proof of Inequality using AM-GM
negative_passages.docid: 81203
negative_passages.text: Supremum and infimum of sets
negative_passages.docid: 127123
negative_passages.text: Cardinality of power set and binary sequence
negative_passages.docid: 156176
negative_passages.text: Lebesgue measurability of nearly identical sets
negative_passages.docid: 134049
negative_passages.text: Showing an inequality is valid
negative_passages.docid: 132595
negative_passages.text: $\sup_{0 \leq M \leq I_{\mathcal{H}_1}} \frac{\operatorname{Tr}[\rho M]}{\operatorname{Tr}[\sigma M]}$ satisfies Data Processing Inequality
negative_passages.docid: 26572
negative_passages.text: Does the Symmetric difference operator define a group on the powerset of a set?
negative_passages.docid: 20816
negative_passages.text: Inequalities with assumptions and constraints
negative_passages.docid: 133082
negative_passages.text: In Peano arithmetic, can we define inequality using successor?
negative_passages.docid: 106979
negative_passages.text: Prove the inequality and limitation
negative_passages.docid: 1316
negative_passages.text: Reverse Triangle Inequality in vector space
negative_passages.docid: 94672
negative_passages.text: Why is the triangle inequality property important for metric spaces?