1. Representation of set (1)Listing elements, One way is to list all the elements of a set when this is possible Example: The set A of odd positive integers less than 10 can be expressed by A={1,3,5,7,9}。 B=x1, x31
1. Representation of set (1)Listing elements, One way is to list all the elements of a set when this is possible.. Example：The set A of odd positive integers less than 10 can be expressed by A={1, 3, 5, 7, 9}。 B={x1 ,x2 ,x3 } √
(2)Set builder notion: We characterize the property or properties that the elements of the set have in common. Example: The set A of odd positive integers less than 10 can be expressed by A=xx is an odd positive integer less than 10 Example: C=xx=y yEZ+) C describes the set of all cubes of positive integers D={x-1<x<2}
( 2 ) Set builder notion: We characterize the property or properties that the elements of the set have in common. Example:The set A of odd positive integers less than 10 can be expressed by A={x|x is an odd positive integer less than 10} Example:C={x|x=y3 ,yZ+ } C describes the set of all cubes of positive integers. D={x|-1<x<2}
(rEcursive definition Recursive definitions of sets have three steps: 1)Basic step: Specify some of the basic elements in the set 2)recursive step: Give some rules for how to construct more elements in the set from the elements that we know are already there 3)closed step: There are no other elements in the set except those constructed using steps 1 and 2
(3)Recursive definition Recursive definitions of sets have three steps: 1)Basic step: Specify some of the basic elements in the set. 2)recursive step: Give some rules for how to construct more elements in the set from the elements that we know are already there . 3) closed step: There are no other elements in the set except those constructed using steps 1 and 2