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

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

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What is a function?

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

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

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

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

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

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Properties of functions

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

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

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

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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

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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

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Sequences

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Inverses

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Next class Proof techniques Read section 3.5 in Jenkyns, Stephenson

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1.6 Functions. Chapter 1, section 6 Functions notation: f: A B x in A, y in B, f(x) = y. concepts: –domain of f, –codomain of f, –range of f, –f maps.

1.6 Functions. Chapter 1, section 6 Functions notation: f: A B x in A, y in B, f(x) = y. concepts: –domain of f, –codomain of f, –range of f, –f maps.

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