1. CSE 20 DISCRETE MATH Prof. Shachar Lovett http://cseweb.ucsd.edu/classes/wi15/cse20-a/ Clicker frequency: CA

2. Todays topics Functions One-to-one, onto, bijective Sequences Inverse function Section 2.2 in Jenkyns, Stephenson

3. What is a function?

4. Is the following a function from X to Y? A. Yes B. No XY

5. What is a function? Is the following a function from X to Y? A. Yes B. No XY

6. What is a function? Is the following a function from X to Y? A. Yes B. No XY

7. What is a function? Is the following a function from X to Y? A. Yes B. No X Y

8. What is a function? Is the following a function from Y to X? A. Yes B. No X Y

9. Properties of functions

12. One-to-one, onto, bijective… XY Is the following function A. One-to-one B. Onto C. Both (bijective) D. None

13. One-to-one, onto, bijective… XY Is the following function A. One-to-one B. Onto C. Both (bijective) D. None

14. One-to-one, onto, bijective… XY Is the following function A. One-to-one B. Onto C. Both (bijective) D. None

15. One-to-one, onto, bijective… Which of the following functions f:N  N is not injective A. f(x)=x B. f(x)=x 2 C. f(x)=x+1 D. f(x)=2x E. None/other/more than one

16. One-to-one, onto, bijective… Which of the following functions f:N  N is not surjective A. f(x)=x B. f(x)=x 2 C. f(x)=x+1 D. f(x)=2x E. None/other/more than one

17. Sequences

18. Inverses

23. Next class Proof techniques Read section 3.5 in Jenkyns, Stephenson