80-110 The Nature of Mathematical Reasoning

Thursday, February 1, 2001

Quiz 2

    Name: _______________________________

  1. When are two lengths commensurable?

  2. Two lenghts AB and CD are commensurable if they can be measured by the same unit. Formally: if there exists a rational number u and natural numbers x and y, such that u*x=AB and u*y= CD. (Lecture).

  3. What is so special about 60 that it has become the base of many number systems?

  4. 60 has many divisors (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60); it is also related to early calendars (with 360 days); but, ultimately, the author does not know. (Barrow, page 65-67).

  5. When is an argument deductively valid?

  6. An argument is deductively valid, if it is impossible for the premises to be true and for the conclusion to be false at the same time (Lecture; FOL, p.24).

  7. What is an inductive argument?

  8. An argument where the truth of the premises make the conclusion more likely to be true (Lecture).

  9. What is the general structure of an argument of the form of modus ponens?

  10. A          A->B
    ----------  (Weston, page 47).