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- 1. Number SystemsThe Real Number Systems
- 2. Objectives:• To determine what qualifies something as a mathematical object.• To develop some of the basic properties of numbers and number systems
- 3. Are phone numbers consideredmathematical objects?
- 4. Number System• A set of objects used together with operations that satisfy some predetermined properties.Objects: 0, 1, 2, -4, 0.6, ⅔, IVOperations: +, - , , ÷Properties: = , > , < , ≠
- 5. Before we invented calculators andelectricity, how did the earliest cultures usemath?
- 6. Number Symbols
- 7. Natural NumbersAre also called the counting numbers because theyare the numbers we use to count with.N: 1, 2, 3, 4, 5,…These numbers were originally used the keep trackof the number of animals, as rankings (1st place, 2ndplace, 3rd place, etc.), or creating calendars.What kinds of numbers are missing from this set?
- 8. Whole NumbersThis set of numbers is the same as the set ofnatural (counting) numbers except for thesymbol to represent nothing (0).W: 0, 1, 2, 3, 4, 5…Besides representing nothing, what otherimportant role does the symbol 0 have in ourcurrent number system?
- 9. Limitations of Natural and Whole #s1) If we add together any two whole numbers, isthe result always a whole number?2) If we subtract any two whole numbers, is theresult always a whole number?3) If we multiply any two whole numbers, is theresult always a whole number?4) If we divide any two whole numbers, is theresult always a whole number?
- 10. IntegersThis set of numbers includes the set of wholenumbers and the negative integers, which arevalues below zero.Z: … -3, -2, -1, 0, 1, 2, 3,…Why do you think we need negative numbers?Where do we see them in our daily lives?
- 11. Limitations of the Integers1) If we add together any two integers, is theresult always a integer?2) If we subtract any two integers, is the resultalways a integer?3) If we multiply any two integers, is the resultalways a integer?4) If we divide any two integers, is the resultalways a integers?
- 12. … - 3, - 2, - 1 0 1, 2, 3…Integers Natural Numbers Whole Numbers
- 13. Use a calculator to evaluate each of the fractionsbelow. Write down the first 6 decimal places. Ifit appears to be a repeating decimal write it withthe bar symbol (i.e. )
- 14. Fractions are written in the formwhere a is called the numerator and b is calledthe denominator. The denominator tells us howmany equal parts the whole is broken into andthe numerator tells us how many parts we have.
- 15. Collins Writing (Type I -1 point):Most algebra textbooks define rational numbersas the quotient of two integers. Using yourknowledge of rational numbers and these terms,to write a definition for rational numbers in yourown words.
- 16. All rational numbers can be written as a fractionor a decimal. However, only repeating orterminating (ending) decimals can be written asa fraction (i.e. as a rational number). We willlearn about decimals that do not have thesecharacteristics in the next section.
- 17. Irrational numberscannot be written as afraction. This set of numbers include non-repeating and non-terminating decimals.

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