Set Theory - Question 2. 0.0 / 5 ? MathematicsSet Theory and Topology.UniversityNone Created by: Lara_BryceCreated on: 18-04-19 21:10 When do A and B have the same cardinal number (or #(A))? If A is equivalent to B; A~B. 1 of 11 When is #(A) = #(B)? If and only if A ~ B. 2 of 11 When is #(A) ≤ #(B)? If and only if A ≤ B. 3 of 11 What is the Schroeder-Bernstein now? If #(A) ≤ #(B) and #(B) ≤ #(A), then #(A) = #(B). 4 of 11 What is the Schroeder-Bernstein theorem? If A ≤ B and B ≤ A, then A~B; let X¡ ¢ Y ¢ X and let X~X¡, then X~Y. 5 of 11 What is a countable set? If and only if a set is finite or denumerable. 6 of 11 When is a set equivalent to N? If and only if a set X is denumerable and has cardinality No. 7 of 11 What is Cantor's Theorem? The power set P(A) of any set A has cardinality greater than A. 8 of 11 What conditions have to be satisfied for a relation ≤ to be a partial order? If and only if for every a,b,c e A: the relation is reflexive, anti-symmetric and transitive. 9 of 11 What does this mean? If and only if for every a ,b, c e A: a ≤ a; a ≤ b and b ≤ a implies a=b; a ≤ b and b ≤ c implies a=c. 10 of 11 What does totally ordered set mean? Partially ordered set if, for every a, b e A, either a ≤ b or b ≤ a. 11 of 11
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