SelfAssessment1 - A, B, C , and two functions f : A B , g :...

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Self-Assessment 1 – Math 117, Spring 2009 Answer the following questions without looking in the book. If you do not feel comfortable answering them, read the corresponding sections in the book, and then solve the problems, again without looking in the book. 1. Let S R . Give the deFnition of a lower bound of S . 2. Let A and B be nonempty subsets of R . Give the deFnition of a function from A to B . 3. Given two sets A, B , and a function f : A B , deFne what it means for f to be injective, surjective, and bijective. 4. Given three sets,
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Unformatted text preview: A, B, C , and two functions f : A B , g : B C , deFne what g f is. If g f is injective, what can we say about f and g ? What if g f is surjective? 5. Prove that Z n and Z are equinumerous for all n N . 6. Show by induction that for any positive real numbers a 1 , . . . , a n , ( a 1 . . . a n ) 1 /n a 1 + + a n n . (1) 7. Show that every real number is the limit of a sequence of rational numbers. 1...
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