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CSE 20 DISCRETE MATH Prof. Shachar Lovett Clicker frequency: CA.

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Presentation on theme: "CSE 20 DISCRETE MATH Prof. Shachar Lovett Clicker frequency: CA."— Presentation transcript:

1 CSE 20 DISCRETE MATH Prof. Shachar Lovett 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

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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

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


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