80-110 The Nature of Mathematical Reasoning

Thursday, February 22, 2001

Quiz 5

    Name: _______________________________

  1. If I say "X is valid", what does X have to be? (Statement, axiom system, proposition, argument, etc.)

  2. An argument. (Lecture).

  3. When is an axiom independent of other axioms?

  4. An axiom of a consistent axioms system is independent if its negation together with the remaining axioms is still consistent. Another way to say this is that the axiom cannot be proved from the other axioms. (Lecture).

  5. Is the axiom system consisting of Euclid's first four axioms and the negation of his fifth axiom consistent?

  6. Yes. One can present models for Non-Euclidean geometries. (Lecture).

  7. In what century where the axioms for arithmetic formulated?

  8. In the 19th century: 1888 by Dedekind, and 1889 by Peano. (Lecture).

  9. In Tarski's World, can an object have more than one name? How about in our (the actual, real) world?

  10. Yes in both cases. (Lecture).