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## Math 330 - 03 Homework (Fall 2018)

• LaTeX-ed solutions are encouraged and appreciated.
• If you use LaTeX, hand-in a printed version of your homework.
• You are encouraged to discuss homework problems with classmates, but such discussions should NOT include the exchange of any written material.
• Writing of homework problems should be done on an individual basis.
• References to results from the textbook and/or class notes should be included.
• The following lists should be considered partial and tentative lists until the word complete appears next to it.
• Use 8.5in x 11in paper with smooth borders. Write your name on top of each page. Staple all pages.


Problem Set 12 (complete) Due: 11/19/2018. Board presentation: 11/??/2018

1. Prove Prop. 10.17
2. Prove Prop. 10.23.iii

Problem Set 11 (complete) Due: 11/12/2018. Board presentation: 11/16/2018

1. Prove the following corollary to Prop. 10.4
Corollary: $\glb(\R^+)=0$.
2. Prove Prop. 10.7
3. Prove Prop. 10.10.iii
4. Prove Prop. 10.13.ii

Problem Set 10 (complete) Due: 11/05/2018. Board presentation: 11/14/2018

1. Let $f:A\to B$ and $g:B\to C$ be functions.
1. If $g\circ f$ is injective, then $f$ is injective.
2. If $g\circ f$ is surjective, then $g$ is surjective.
2. Construct examples of functions $f:A\to B$ and $g:B\to C$ such that:
1. $g\circ f$ is injective, but $g$ is not injective.
2. $g\circ f$ is surjective, but $f$ is not surjective.
3. Prove Prop. 9.15 (Hint: induction)
4. Prove Prop. 9.18