Day 4: mat385

• Hand back homework 1.1.
  • I graded #8/9, 10/11
  • Homework is graded out of 4 points
  • Make sure that you check your answers in the back of the book when possible! That's legit....

• Collect homework 1.2.

• Continuing with section 1.3 (pdf): Quantifiers, Predicates, and Validity

• Questions on problems from section 1.3 homework?

• Section 1.4 (pdf): Predicate logic

Links:

• What does it mean when one says that "The domain is the whole world."? (e.g. p. 43, problem 11).

  On a set containing all sets: Russell's paradox.

  "Russell's paradox is the most famous of the logical or set-theoretical paradoxes. The paradox arises within naive set theory by considering the set of all sets that are not members of themselves. Such a set appears to be a member of itself if and only if it is not a member of itself, hence the paradox.

  "Some sets, such as the set of all teacups, are not members of themselves. Other sets, such as the set of all non-teacups, are members of themselves. Call the set of all sets that are not members of themselves S. If S is a member of itself, then by definition it must not be a member of itself. Similarly, if S is not a member of itself, then by definition it must be a member of itself. Discovered by Bertrand Russell in 1901, the paradox has prompted much work in logic, set theory and the philosophy and foundations of mathematics."