# Natural number: Quiz

Question 1: Analogously, given that addition has been defined, a ________ × can be defined via a × 0 = 0 and a × S(b) = (a × b) + a.
MultiplicationExponentiationVector spaceAlgebra

Question 2: Properties of the natural numbers related to divisibility, such as the distribution of prime numbers, are studied in ________.
Analytic number theoryAlgebraMathematicsNumber theory

Question 3: Essays on the Theory of Numbers by Richard Dedekind at ________
Project Gutenberg AustraliaProject GutenbergAmazon KindleGoogle Books

Question 4: Natural numbers have two main purposes: ________ ("there are 6 coins on the table") and ordering ("this is the 3rd largest city in the country").
Countable setCardinal numberSet theoryCounting

Question 5: With these definitions it was convenient to include 0 (corresponding to the ________) as a natural number.
Set (mathematics)Set theoryEmpty setTopological space

Question 6: Certain constructions show that, given ________, models of the Peano postulates must exist.
Mathematical logicFirst-order logicGeorg CantorSet theory

Question 7: The rank among well-ordered sets is expressed by an ________; for the natural numbers this is expressed as "ω".
Ordinal numberCardinal numberSurreal numberReal number

Question 8: (Sometimes, an index or ________ "+" is added to signify "positive".
Subscript and superscriptDashTypefaceOpenType

Question 9: Furthermore, one defines a ________ on the natural numbers by writing a ≤ b if and only if there exists another natural number c with a + c = b.
Total orderOrder theoryPartially ordered setBinary relation

Question 10: A standard construction in ________, a special case of the von Neumann ordinal construction, is to define the natural numbers as follows:
Model theoryMathematical logicSet theoryGeorg Cantor