Integrated Math Section 1.2 Real Numbers

Notecard definitions Natural numbers- (N) set of counting numbers {1,2,3,4,5,6…} Whole numbers- (W) set of natural numbers plus zero (the hole) {0,1,2,3,4,5…} Integers- (Z) set of whole numbers and all their opposites {… -4,-3,-2,-1,0,1,2,3,4…}

https://www.youtube.com/watch?v=gb-UqwUZfG4

Natural numbers, whole numbers and integers are dots on a number line A={xl x is a whole number between 4 and 7}

Rational numbers-(Q) any number that can be written as a ratio of two integers The set is impossible to list! You must use set-builder notation. Q= {x| 𝑎 𝑏 𝑎 𝑎𝑛𝑑 𝑏 𝑎𝑟𝑒 𝑖𝑛𝑡𝑒𝑔𝑒𝑟𝑠, 𝑤𝑖𝑡ℎ 𝑏≠0}

Examples of rational numbers 8= 8/1 .333… = 1/3 0 = 0/1 -5/3 -8/-11 All repeating non-terminating decimals

Irrational numbers- (I) numbers that cannot be expressed as a ratio Irrational numbers- (I) numbers that cannot be expressed as a ratio. They do not repeat and do not terminate.

Irrational numbers are loners! They don’t belong with the other groups of numbers. They are usually stuck under a radical sign. They are real.

A well known irrational number is ________.

Real numbers- (R) the union of the set of rational numbers and irrational numbers R =( Q) ∪ ( I)

Sets of special numbers W= ______________ Z= _____________ Q= _____________ I= _____________ R= _____________

Is Z a subset of R? yes Is 4/5 ∈ Z? no Is 𝜋 ∈ I? Is Z ∪ I = I? Is I ∩ Q = ∅?

Consider this set A={ all natural numbers less than 4} What is the list of elements in the set?

Interval notation (used for real numbers) Parentheses and brackets will be used on the endpoints. Parentheses ( or ) do not include the endpoint Brackets [ or ] include the endpoint (7, 9] means all real numbers greater than 7 and less than or equal to 9

Real numbers are shown as a ray, a line or a segment on the number line. A={xI x is a real number between 3 and 10}

Interval of real numbers-the set of real numbers that lie between two real numbers

An interval of real numbers can not be listed so you can make a line graph or use set-builder notation.

If a number line graph goes to positive or negative infinity, an arrow is used. The interval notation for all real numbers greater than 10 would be (10, ∞) The interval notation for all real numbers less than 10 would be (-∞, 10)

Assignment #2A Pg. 17 #3-87 multiples of 3

Remember Union is joining two sets (everything) Intersection is what two sets have in common

Consider finding the union of two sets of real numbers (4,12]∪(2,10] When doing this problem, it is useful to make to sketches above the number line. Write all the critical numbers on a number line 0 2 4 10 12

(4,12]∪(2,10] 0 2 4 10 12

What would be the solution set to the following What would be the solution set to the following? #1 (9,15) ∪ (7,21) #2 (−∞, 10] ∩ (7,12] *For these problems, make two graphs above the number line, then find the union (everything) or the intersection (the overlap part) and graph on the number line.

#1 starts at 7 ends at 21 (7,21) #2 starts at 8 ends at 10 (8,10] Find the intersection 7,21 ∩(8,10]

Is the following statement true or false? 4,19 ⊂[1,23] A number line can help you answer this question. Write all the critical numbers on the number line Sketch the two intervals Look to see if all the numbers in the smaller set are in the larger set.

Assignment #2B Pg. 18 #91-107 odd