When mathematicians talk about a set, they sometimes want to know how big a set is (or what is the cardinality of the set). They do this by counting how many elements are in the set (how many items are in the bag).
1. To put in a specified position or arrangement; place: set a book on a table; set the photo next to the flowers. 2. a. To put into a specified state: set the prisoner at liberty; set the house ablaze; set the machine in motion. b. To cause to begin an action: The noise set the dog to barking.