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Ordinal number: Quiz

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Question 1: A ________ (which, in this context, includes the number 0) can be used for two purposes: to describe the size of a set, or to describe the position of an element in a sequence.
Real numberCardinal numberNatural numberInteger

Question 2: Any ordinal number can be made into a topological space by endowing it with the ________; this topology is discrete if and only if the ordinal is a countable cardinal, i.e.
Long line (topology)Compact spaceOrder topologySeparable space

Question 3:
Which of the following titles did Ordinal number have?
Mr. Chevy Celebrity
Suburban Myth
Ordinal Number
Is This Thing On?

Question 4: Ordinals were introduced by ________ in 1897 to accommodate infinite sequences and to classify sets with certain kinds of order structures on them.
Mathematical logicGeorg CantorDavid HilbertSet theory

Question 5: x is a transitive set ________ by set inclusion,
Binary relationPartially ordered setTotal orderOrder theory

Question 6: Such a one-to-one correspondence is called an order isomorphism and the two well-ordered sets are said to be order-isomorphic, or similar (obviously this is an ________).
Equivalence relationBinary relationGroup (mathematics)Group action

Question 7: The standard definition, suggested by ________, is: each ordinal is the well-ordered set of all smaller ordinals.
John von NeumannPaul DiracQuantum mechanicsBra-ket notation

Question 8: One justification for this term is that a limit ordinal is indeed the limit in a topological sense of all smaller ordinals (under the ________).
Compact spaceTopological spaceOrder topologyLong line (topology)

Question 9: Ordinals are an extension of the natural numbers different from ________ and from cardinals.
IntegerRational numberNegative and non-negative numbersField (mathematics)

Question 10: For example, every set of ordinals has a ________, the ordinal obtained by taking the union of all the ordinals in the set.
Complete latticeInfimumOrder theorySupremum







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