ECS 20 Study Guide - Comprehensive Final Exam Guide - Integer, Permutation, Sum Rule In Differentiation

• School: UC-Davis
• Department: Engineering: Computer Science
• Course: ECS 20
• Professor: All

Document Summary

Set theory: a set is a well-defined collection of objects. Notation: (cid:1827),(cid:1828),(cid:1829),(cid:1845), for set (cid:1845) (cid:1853),(cid:1854),(cid:1855) for element (cid:1845: (cid:1853)(cid:1488)(cid:1845) element (cid:1853) is in the set (cid:1845) (cid:1853)(cid:1489)(cid:1845) (cid:1853) is not an element of (cid:1845, specify (cid:1853) set, by listing is elements, for example(cid:1827)={(cid:883),(cid:885),5,(cid:889),(cid:891)} For example (cid:1827)={| is an odd integer and less than (cid:883)(cid:882)} Where (cid:1827) is a set and is an element: vann diagram-pictorial representation (not rigorous, by showing those properties which characterizes the elements in the set. Elements: subset: consider sets (cid:1827) and (cid:1828) (cid:1827) (cid:1828) every (cid:1488)(cid:1827),(cid:1488)(cid:1828) (cid:1827) is a subset of (cid:1828) Empty set for example (cid:1845)={| is a positive integer of (cid:2870)=(cid:885)}= (cid:1827) Independent law (cid:1827)(cid:1515)(cid:1827)=(cid:1827) and a(cid:1514)a=a: associative law (cid:4666)(cid:1827)(cid:1515)(cid:1828)(cid:4667)(cid:1515)(cid:1829)=(cid:1827)(cid:1515)(cid:4666)(cid:1828)(cid:1515)(cid:1829)(cid:4667, a set (cid:1845) is finite if (cid:1845) is empty or (cid:1845) contains exactly (cid:3021) elements (cid:3021) is a positive integer, = cardinality of (cid:1845)