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Transcript

Lesson 2.1 Basic Set Concepts • A set is a collection of objects whose contents can be clearly determined. • Elements, or members, - the objects in a set • Capital letters are used to name sets. • Methods to name sets: 1) word description 2) roster method 3) set builder notation • Roster method lists all elements in braces { } • Write a word description for the set. L = {a, b, c, d, e} • Set builder notation – Lets express days of the week in s.b.n W = {x| x is a day of the week • Express in roster and set builder notation. • M is the set of all months beginning with the letter M. • The empty set, or null set, contains no elements. Represented by { } or ø. – {x|x is greater than 8 and less than 2 • The symbol is used to indicate that an object is an element of a set. • True or false • v {a, b, c … z ) -3 • The set of Natural numbers N = {1,2,3,4 ……} {1, 2, 3, ….} • The number of elements in a set is called the cardinal number, or cardinality, of the set. • L = {a,e,i,o,u} has cardinality of 5 • Symbol n(L) is read “n of L.” • Repeating Elements in a set does not add to the cardinality of a set. • If set A is equivalent to set B, then set A and B contain the same number of elements. n(A) = n(B) Example If set A is equal to set B then, A and B contain exactly the same elements, regardless of order or possible repetition. A=B example • Finite set – has a definite number of elements • Infinite set – doesn't have a set number of elements • Examples