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# 1.1 Real Numbers and their Graphs read ## 1.1 Real Numbers and their Graphs read

This post you will find information about – 1.1 Real Numbers and their Graphs read • Sets of Numbers,
• Equality, Inequality Symbols, and variables
• The Number Line
• Graphing Subsets of the Real Numbers
• Absolute Value of a Number

Sets of Numbers

A set is a collection of objects. For example, the set {1,2,3,4, 5} Read as “the set with decimals 1, 2, 3, 4 and 5.”

contains the numbers 1, 2, 3, 4, and 5. The members or elements in a set are listed with braces { }.

Two basic sets of numbers

Natural Set of Numbers (Positive Integers) { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, …}

The Set of Whole Numbers {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, …}

The three dots are called ellipses indicates that each list continues forever.

Use examples include, some vehicles might get 35 miles per gallon (mpg) of gas, or in metric just under 15 kilometer per liter.

Numbers that indicate a loss are called negative numbers and are shown as – sign. For example a temperature of 15 degrees below zero can be shown as -15 deg.

The Set of Integers {…, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5,…} The negatives of the natural numbers and the whole numbers together form the set of integers.

Because the set of natural numbers and set of whole numbers are included within the set of integers, these sets are called subsets of the set of integers.

However, integers can not describe every real-life event an example, a student may study 2 1/2 hours , or a computer may cost \$432.27. We need fractions to describe these events, more commonly called rational numbers.

The Set of Rational Numbers { All numbers than can be written as a fraction with and integer in its numerator and a nonzero integer in its denominator}

Some examples of rational numbers

3/2, 18/12, -53/9, 0.25, and -0.66666…

The decimals 0.25 and -0.66666… are rational numbers, 0.25 can be written as 1/4, and -0.66666… can be written as the fraction – 2/3.

Every integer can be written as a fraction with a denominator of 1, every integer is also a rational number. Since every integer is a rational number, the set of integers is a subset of the rational number.

π and √ 2 cannot be written as fractions with an integer numerator and a nonzero integer denominator, that are not rational numbers, but are irrational numbers. 