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Cardinal number: Quiz

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Question 1:
Which of the following titles did Cardinal number have?
Cardinal Archbishop Emeritus of Baltimore
Cardinal Priest of San Clemente
Cardinal Number
Louisville Cardinals

Question 2: He also proved that the set of all ________ of natural numbers is denumerable (which implies that the set of all rational numbers is denumerable), and later proved that the set of all algebraic numbers is also denumerable.
Set theoryOrdered pairFunction (mathematics)Set (mathematics)

Question 3: Under the assumption of the ________, this transfinite sequence includes every cardinal number.
Axiom of choiceZermelo–Fraenkel set theorySet theoryMathematical logic

Question 4: However, if we restrict from this class to those equinumerous with X that have the least rank, then it will work (this is a trick due to ________: it works because the collection of objects with any given rank is a set).
Donald KnuthRobin MilnerDana ScottRichard Karp

Question 5: Addition is ________ (κ + μ) + ν = κ + (μ + ν).
CommutativityAlgebraic structureAssociativityDistributivity

Question 6: This sequence starts with the ________ (finite cardinals), which are followed by the aleph numbers (infinite cardinals of well-ordered sets).
IntegerReal numberNatural numberCardinal number

Question 7: Note the element d has no element mapping to it, but this is permitted as we only require a one-to-one mapping, and not necessarily a one-to-one and ________ mapping.
Group (mathematics)Surjective functionFunction (mathematics)Equivalence relation

Question 8: A fundamental theorem due to ________ shows that it is possible for infinite sets to have different cardinalities, and in particular the set of real numbers and the set of natural numbers do not have the same cardinal number.
Mathematical logicSet theoryGeorg CantorDavid Hilbert

Question 9: The ________ is equivalent to the statement that given two sets X and Y, either | X | ≤ | Y | or | Y | ≤ | X |.
Zermelo–Fraenkel set theoryMathematical logicSet theoryAxiom of choice

Question 10: By the ________, this is equivalent to there being both a one-to-one mapping from X to Y and a one-to-one mapping from Y to X.
Cardinal numberGeorg CantorSet theoryCantor–Bernstein–Schroeder theorem







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