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Sets, Maps and Symmetry Groups Course Discussion List


Corrections to the notes

Posted by Albert Wang on October 14, 1999 at 22:13:58:

These are just some minor corrections to Chapter 1, and one correction for chapter 2.

-- on page 7, in the second example about Euclidean closures: "...of a punctured interval of the form [a,b) U (b,c] should be the interval [a,b]." The closed interval should be [a,c] (a change of b to c in a crucial place).

-- on page 9, when explaining power sets the notes read: "That this is always the case is called the Power Set Axiom since the set of all subsets *of subsets* of a given set X is called the power set of X..." The phrase "of subsets" marked off by the *'s should not be there.

-- on page 9, lower down, when explaining about interpreting the Kuratowski Axioms from the point of view of power sets and predicates. "Similarly, Axiom C3 can be viewed in terms of the predicate Q on 2^X such that Q(A) is true if and only if KKA=A. To think of the *third* Axiom this way requires a predicate R defined on pairs of subsets of X so that R(A,B) holds if and only if K(A U B) = KA U KB." The "third" in *'s should be "second," as C2 is the Axiom that involves unions of sets.

For chapter 2:

-- on page 29 (section 2.4, in example 2.6), the power set of Z is listed as the union of A's. It should be the union of the sets of A's. {A1} U {A2} U {A3} instead of A1 U A2 U A3.

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