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 Math for College Readiness

Set Collection of elementsCollection of elements Set-builder notationSet-builder notation notation.htmlhttp:// notation.htmlhttp:// notation.htmlhttp:// notation.html –It says "the set of all x's, such that x is greater than 0". In other words any value greater than 0In other words any value greater than 0 Notes:Notes: The "x" is just a place-holder, it could be anything, such as { q | q > 0 }The "x" is just a place-holder, it could be anything, such as { q | q > 0 } Some people use ":" instead of "|", so they would write { x : x > 0 }Some people use ":" instead of "|", so they would write { x : x > 0 }

InequalitiesInequalities The Number LineThe Number Line Interval NotationInterval Notation intervalnot.htmhttp://regentsprep.org/regents/math/algebra/ap1/ intervalnot.htmhttp://regentsprep.org/regents/math/algebra/ap1/ intervalnot.htmhttp://regentsprep.org/regents/math/algebra/ap1/ intervalnot.htm (see page 2 and 5 in textbook).(see page 2 and 5 in textbook). 3 ways to represent sets

Procedure Using interval Notation The endpoints used in interval notation are always written from left to right. That is, the smaller number is written first, followed by a comma, followed by the larger number.The endpoints used in interval notation are always written from left to right. That is, the smaller number is written first, followed by a comma, followed by the larger number. Parentheses) or (indicate that an endpoint is excluded from the set.Parentheses) or (indicate that an endpoint is excluded from the set. Square brackets ] or [ indicate that an endpoint is included in the set.Square brackets ] or [ indicate that an endpoint is included in the set. Parentheses are always used with ∞ and - ∞. Parentheses are always used with ∞ and - ∞.

Subsets of Real Numbers

Real Numbers continued…

Inequalities

∪ is Union: is in either set∩ ∪ is Union: is in either set∩ ∩ is Intersection: must be in both sets (common)∩ is Intersection: must be in both sets (common) Empty Set: the set with no elements. Shown by {}Empty Set: the set with no elements. Shown by {} diagrams.htmlhttp:// diagrams.htmlhttp:// diagrams.htmlhttp:// diagrams.html Union and Intersection of Sets p. 7

Intermediate Algebra Textbook p #4-26 evens,56Intermediate Algebra Textbook p #4-26 evens,56 Classwork