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Empty product: Quiz

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Question 1: Two often-seen instances are a0 = 1 (any number raised to the zeroth power is one) and 0! = 1 (the ________ of zero is one).
Number theoryGamma functionPrime numberFactorial

Question 2: In any category, the product of an empty family is a ________ of that category.
Category (mathematics)Limit (category theory)Initial and terminal objectsAdjoint functors

Question 3: For similar reasons, the intersection of an ________ of subsets of a set X is conventionally equal to X.
Set (mathematics)Model theoryEmpty setTopological space

Question 4: that is, the singleton set containing the ________.
Set theoryTupleNatural numberSet (mathematics)

Question 5: Using this property as definition, and extending this to the empty product, the right-hand side of this equation evaluates to b0 for the ________, because the empty sum is defined to be zero, and therefore the empty product must equal one.
Set theoryEmpty setSet (mathematics)Topological space

Question 6: The sum of two ________ is equal to the logarithm of the product of their operands, i.e.
LogarithmExponentiationGroup (mathematics)Natural logarithm

Question 7: (A programmer may, of course, implement it.) Languages implementing ________ are the exception.
Programming languageC (programming language)Variadic functionJava (programming language)

Question 8: In set theory and combinatorics, the ________ nm is the size of the set of functions from a set of size m into a set of size n.
Ordinal numberCardinal numberNatural numberGeorg Cantor

Question 9: Dually, the ________ of an empty family is an initial object.
Initial and terminal objectsProduct (category theory)Limit (category theory)Coproduct

Question 10: Consider the general definition of the ________:
Cardinal numberCartesian productDirect productBinary relation







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