Material Taken From: Mathematics for the international student Mathematical Studies SL Mal Coad, Glen Whiffen, John Owen, Robert Haese, Sandra Haese and Mark Bruce Haese and Haese Publications, 2004

Homework Policy Late homework will not be accepted Graded in one standard If based on completion… 100% complete = 6 80%-99% complete = 5 60%-79% complete = 4 40%-59% complete = 3 20%-39% complete = 2 0%-19% complete = 0

Chapter 1 Number Sets and Properties Wednesday, Aug 18 th - Sections ABC Friday, Aug 20 th – Sections DEF Tuesday, Aug 24 th – Section G and Review Thursday, Aug 26 th – Chapter 1 Quiz

Section A – Some Set Language A set is a collection of numbers or objects. - If A = {1, 2, 3, 4, 5} then A is a set that contains those numbers. An element is a member of a set. - 1,2,3,4 and 5 are all elements of A. -  means ‘is an element of’ hence 4  A. -  means ‘is not an element of’ hence 7  A. -  means ‘the empty set’ or a set that contains no elements.

Subsets If P and Q are sets then: – P  Q means ‘P is a subset of Q’. – Therefore every element in P is also an element in Q. For Example: {1, 2, 3}  {1, 2, 3, 4, 5} or {a, c, e}  {a, b, c, d, e}

Union and Intersection P  Q is the union of sets P and Q meaning all elements which are in P or Q. P ∩ Q is the intersection of P and Q meaning all elements that are in both P and Q. A = {2, 3, 4, 5} and B = {2, 4, 6} A  B = A ∩ B =

M = {2, 3, 5, 7, 8, 9} and N = {3, 4, 6, 9, 10} True or False? I.4  M II.6  M List: I.M ∩ N II.M  N Is: I.M  N ? II.{9, 6, 3}  N?

Reals Rationals Integers (…, -2, -1, 0, 1, 2, …) Natural (0, 1, 2, …) Counting (1, 2, …) Irrationals Section B – Number Sets (fractions; decimals that repeat or terminate) (no fractions; decimals that don’t repeat or terminate) * +

Section B – Number Sets N* = {1, 2, 3, 4, …} is the set of all counting numbers. N = {0, 1, 2, 3, 4, …} is the set of all natural numbers. Z = {0, + 1, + 2, + 3, …} is the set of all integers. Z+ = {1, 2, 3, 4, …} is the set of all positive numbers. Z- = {-1, -2, -3, -4, …} is the set of all negative numbers. Q = { p / q where p and q are integers and q ≠ 0} is the set of all rational numbers. R = {real numbers} is the set of all real numbers. All numbers that can be placed on a number line.

1.Show that 0.45 is rational. 2.Show that … is rational.

Section C – Words Used in Mathematics Sum = Difference = Product = Quotient = Terms = numbers being added or subtracted Factors = numbers that divide exactly into another number Divisor = the number by which we divide Dividend = the number being divided Note: product and quotient can also refer to the result as well as the action.

Find the Sum of 233, 42 and 6