Jamie M., Meg P., Emily P. The Real Number System Properties of Real Numbers Subsets Empty Sets Complements The real number system is almost like a school (like you would see in movies). All the "students" are split up into different groups. The different groups are natural numbers, whole numbers, integers, rational numbers, and irrational numbers. The Real Number System In a school setting, you can think of the natural numbers as "the snobs." They will only include the numbers 1,2,3,etc. on to infinity and beyond. The Natural Numbers The whole numbers we like to think of as "the jocks." Whole numbers start to include 0. So their order goes 0,1,2,3,etc. The Whole Numbers Integers are the next group in the real number system. In a school setting, we like to think of them as "negative nellies." We gave them this name because this group involves the negative numbers. Their order goes from negative infinity to positive infinity (-5,-4,-3,-2,-1,0,1,2,3,etc...) Integers After the integers come the rational numbers. Rational numbers are "the geeks." Rational numbers can be decimals or fractions as long as the terminate or repeat. For example, a rational number would be something like 0.75 or 0.333. Rational Numbers Next are irrational numbers or as we like to call them, "the creative optimists." Irrational numbers can be fractions or decimals too, but they DO NOT terminate or repeat. For example, an irrational number can be pi or 0.125678941. Irrational Numbers We all know what a set is (a collection of elements). We also know that we put our sets in brackets { }. Well, we can think of a set as our universe. The universe is split into different galaxies, right? Those galaxies are subsets. For example, if the set was {1,2,3,5,6,8}, an example of a subset would be {1,2,3}. Another example of a subset would be {1,3,5}.

My subsets were only three numbers, but subsets can have any amount of numbers. Remember, all numbers that you put in a subset have to be members of the original set. Subsets Empty set, also called the null set, is exactly what it sounds like. A set that's empty. Empty sets use the symbols {} or by the symbol shown below. Empty sets can also be categorized as a subset. Empty Set Next is complements. Now, to explain complements we should use sets. Set A and set B. Set A is {1,2,3,4,5,6} and set B is {2,4,6}. A complement is any numbers in set A that aren't in set B. So the complement here is {1,3,5}. Complements also go in the brackets { }. Complement There are six properties of real numbers. They are the communitive, associative, distributive, identity, inverse, and zero-product properties. Properties of Real Numbers The communitive property basically states that order does not matter. Say you have 3+2=6. It would still work if you plugged in 2+3=6. You still end up with the same answer. It's like a GPS. It may give you many different ways to get somewhere, but you'll always end up at that one location. Communitive Property The associative property states that grouping doesn't matter when you have parentheses. Say you had (3+2)+5=10. It would be the same if you switched the parentheses to 3+(2+5)=10. Take an association for example. There are tons of different groups of people they are all working for the same cause. Associative Property The distributive property needs an example to be explained. Say you have a=2(5+6). You would first do 2x5=10. Then you do 2x6=12. To get the answer you would then add 10+12=22. That's how you do the distributive property. Distributive Property a=2(5+6) a=10+12 a=22 This property states that if you multiply a number by 1, you will get the same number. If you add 0 to a number, you will get that same number. Just think of yourself. If you add nothing (0) to yourself, you stay the same. If you multiply yourself by 1 (yourself+yourself) you're obviously going to get yourself. Identity Property 5x1=5 3+0=3 The next property is the additive inverse property. The additive inverse is basically any negative number plus it's absolute value (positive of the same number) equals zero. For example,

-5+5=0. Additive Inverse Property Multiplicative inverse is when you multiply a number by its reciprocal it equals 1. For instance... Multiplicative Inverse 3 x 1/3 = 1 Last but not least is the zero-product property. This one is simple... if you multiply any number by 0 you automatically end up with 0. Zero-Product Property 1,000,000 x 0 = 0 Set builder notation involves the number line. You see, you put set builder notation in brackets { } also. Also, you write it like so {x:x < 3}. Now, this means "the set of all x such that x is less than 3." In other words, x is less than 3. Set Builder Notation Interval notation is another way to show the graph on a number line. This notation uses parentheses ( ) and brackets [ ]. Say you had x < 3 on your number line... Interval Notation & Inclusive and Exclusive -1 -2 -3 0 1 2 3 You would put this into interval notation like so

( , 3). This is because you can't include infinity, which is why you use the parentheses, and you can't include 3 because the circle is open. Inclusive and exclusive are which signs, parentheses or brackets, to put in front of or after the numbers. Parentheses, ( ), mean that the number is NOT included or "exclusive." Brackets [ ] mean that you do include the number or "inclusive."

Open and closed pertains to the circles on the number line. If the circle is open, or not filled in, it means you do NOT include the number. If the circle is closed, or filled in, you do include that number. Inclusive and exclusive & Open and closed. Roster form is really when you list the numbers with commas in between. Like a roster for a sports team, they list they players' names separated. For example, 1, 2, 3, 4, 5, 6 . Roster Form -1 -2 -3 0 1 2 3 Prezi: www.google.com

Pamphlet: www.toondraw.com Works Cited THANKS FOR WATCHING

By;

Meg Pickerell

Emily Perry

&

Jamie Molnar Union is when you take 2 sets and combine them. So, your unionizing the two sets. Take the United States for example. During the Civil War, we were divided into North and South. After the Civil War, we were one union. Let's say that Set A {1, 2, 3, 6} is the North and Set B {1, 2, 4, 5, 7} is the South. After the Civil War, they would combine and turn into A U B {1, 2, 3, 4, 5 ,6, 7}. The symbol U is used to symbolize a union. So A U B means the union of set A and set B. Union Intersection, unlike union, is a set of numbers that the 2 sets have in common. Say you have set A {1, 2, 3, 4, 6} and set B {2, 4, 6, 8}. The Intersection would be {2, 4, 6} because both sets have those numbers. Intersection The Amazing Meg Pickerell

The Glorious Emily Perry

&

Jamie Molnar the Great Real Number System, Subsets, Inequalities and Much More in this Incredible Work By: Inequalities are a way of showing if a number is greater than, less than, or equal to another number or x. < means less than, > means greater than, and of course = means equal to. Inequalities For Example:

3 < 10 (3 is less than 10)

12 > 9 (12 is greater than 9)

15 = 15 (15 is equal to 15)

You can also say 15 = 7+8 because the sum of 7 and 8 is 15.

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# Real Number System Presentation

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