Math 350 Homework Solutions Section 7 FUNCTIONS
Advanced Calculus I
Fall 2009
7.7 Classify each function as injective, surjective, bijective, or none of these. (e) f : N Z dened by f (n) = n2 n. Injectivity. This function is injective but not surjective.
Math 350 Homework Solutions Section 8 CARDINALITY Text Problems
Advanced Calculus I
Fall 2009
8.10 Prove: For all sets S , if S is denumerable, then S is equinumerous with a proper subset of itself. Proof: Suppose S is denumerable. We need to show there e
Math 350 Homework Solutions 1 Textbook Chapter 7
Advanced Calculus I
Spring 2008
7.7 Classify each function as injective, surjective, bijective, or none of these. (a) f : N Z defined by f (n) = n2 - n Solution This function is injective but not s
Math 350 Homework Solutions 3 # 1:
Advanced Calculus I
Spring 2008
Supplementary Problem A Let S R be a nonempty and bounded set. Let m = sup S. Prove: If m S, then S has no maximum. This result can be used in Problem 12.3.
Solution We prove th
Math 350 Advanced Calculus I Homework Solutions Section 13 TOPOLOGY OF THE REALS 13.3 Find the interior of each set.
Fall 2009
13.4 Find the boundary of each set. 1 (a) |nN n Since int S S , then the only possible interior points of the set are the elemen
Math 350 Homework Solutions 4
Advanced Calculus I
Spring 2008
# 1-3: Textbook Chapter 13 13.14 Let S be a bounded infinite set and let x = sup S. Prove: If x S, then x S . / Solution Suppose x S. We need to show x S . That is, we need to show
Math 350 Advanced Calculus I Homework Solutions Section 12 THE COMPLETENESS AXIOM
Fall 2009
12.3 For each of the following subsets of R, give its supremum and its maximum, if they exist. For each part, you must verify your results. That is, if you are cla
Math 350 Advanced Calculus I Homework Solutions Section 11 ORDERED FIELDS
Fall 2009
11.3 Let x, y , and z be real numbers. Prove the following. (a) (x) = x Proof: The element (x) is by denition the additive inverse of x. To show (x) = x, we need to show t
Math 350 Homework Solutions Section 8 CARDINALITY Text Problems
Advanced Calculus I
Fall 2009
8.3 Show that each of the following pairs of sets S and T are equinumerous by nding a specic bijection between them. (a) S = [0, 1] and T = [1, 3] We need a func
Math 350 Homework Solutions 2 1-2:Textbook 8
Advanced Calculus I
Spring 2008
1. (8.3) Show that each of the following pairs of sets S and T are equinumerous by finding a specific bijection between them. a S = [0, 1] and T = [1, 3] Solution We need