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

2. Todays topics Set sizes Set builder notation Set rapid-fire quiz Section 2.1 in Jenkyns, Stephenson

3. Power set size Let A be a set of n elements: |A|=n How large is P(A), the power-set of A? A. |P(A)| = n B. |P(A)| = 2n C. |P(A)| = n 2 D. |P(A)| = 2 n E. None/other/more than one

4. Union size

5. Intersection size

6. Cartesian product size

7. Important sets of numbers Z = integers Z = {…,-3,-2,-1,0,1,2,3,…} N = natural numbers = positive integers N = {1,2,3,…} Q = rational numbers Q = {x/y : x,y  Z}

8. Set builder notation

10. Ways of defining a set Enumeration: {1,2,3,4,5,6,7,8,9} + very clear - impractical for large sets Incomplete enumeration (ellipses): {1,2,3,…,98,99,100} + takes up less space, can work for large or infinite sets - not always clear {2 3 5 7 11 13 …} What does this mean? What is the next element? Set builder: { n | } + can be used for large or infinite sets, clearly sets forth rules for membership

11. Primes Enumeration may not be clear: {2 3 5 7 11 13 …} How can we write the set Primes using set builder notation? A. {n  N :   a,b  N, n=ab} B. {n  N :  a,b  N, n=ab  (a=1  b=1)} C. {a,b  N :  n  N, n=ab  (a=n  b=n)} D. {n  N :  a,b  N, n=ab  (a=1  b=1)} E. None/other/more than one

12. Russell’s paradox Let A={S| S  S} Does A  A? A. Yes B. No C. Neither D. Both E. Other

13. Russell’s paradox

14. Set Theory rapid-fire practice

17. Next class Functions, sequences Read section 2.2 in Jenkyns, Stephenson