Section 1.1

Objective: Sets of Numbers and Interval Notation

The student will be able recognize basic definitions and notations used to express

algebraic relationships.

Mrs. Carruthers Mrs. Carruthers Math for College ReadinessMath for College Readiness

SetSet

• Collection of elements Collection of elements • Set-builder notationSet-builder notation• http://www.mathsisfun.com/sets/set-builder-http://www.mathsisfun.com/sets/set-builder-

notation.htmlnotation.html– It says It says "the set of all x's, such that x is greater "the set of all x's, such that x is greater

than 0"than 0"..• In other words In other words any value greater than 0any value greater than 0• Notes:Notes:• The "x" is just a place-holder, it could be The "x" is just a place-holder, it could be

anything, such as anything, such as { q | q > 0 }{ q | q > 0 }• Some people use "Some people use "::" instead of "" instead of "||", so they ", so they

would write would write { x : x > 0 }{ x : x > 0 }

• Inequalities Inequalities

• The Number Line The Number Line

• Interval NotationInterval Notation

• http://regentsprep.org/regents/math/http://regentsprep.org/regents/math/algebra/ap1/intervalnot.htmalgebra/ap1/intervalnot.htm

• http://www.mathsisfun.com/sets/http://www.mathsisfun.com/sets/intervals.htmlintervals.html

• (see page 2 and 5 in textbook).(see page 2 and 5 in textbook).

3 ways to represent sets3 ways to represent sets

Procedure Using interval NotationProcedure Using interval Notation

• The endpoints used in interval notation are The endpoints used in interval notation are always written from left to right. That is, the always written from left to right. That is, the smaller number is written first, followed by smaller number is written first, followed by a comma, followed by the larger number.a comma, followed by the larger number.

• Parentheses) or (indicate that an endpoint Parentheses) or (indicate that an endpoint is excluded from the set.is excluded from the set.

• Square bracketsSquare brackets] or [ indicate that an endpoint is ] or [ indicate that an endpoint is included in the set.included in the set.

• Parentheses are always used with ∞ and - ∞ .Parentheses are always used with ∞ and - ∞ .

Subsets of Real NumbersSubsets of Real Numbers

Real Numbers continued…Real Numbers continued…

InequalitiesInequalities

• ∪∪ is Union: is in either setis Union: is in either set∩∩

• ∩∩ is Intersection: must be in both sets is Intersection: must be in both sets (common)(common)

• Empty Set: the set with no elements. Empty Set: the set with no elements. Shown by {}Shown by {}

• http://www.mathsisfun.com/sets/venn-http://www.mathsisfun.com/sets/venn-diagrams.htmldiagrams.html

Union and Intersection of Sets p. 7Union and Intersection of Sets p. 7

• Intermediate Algebra Textbook p. 10-12 Intermediate Algebra Textbook p. 10-12 #4-26 evens,56#4-26 evens,56

ClassworkClasswork