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Real Numbers

Radicals

Inequalities & Absolute Value

Polynomials

Rational Expressions 1

Rat'l. Exp. 2 - mult&div

Rat'l. Exp. 3 - add&subt

Slope & Equations of Lines

Review&Test

 

 

 

jdsmathnotes

 


 

 UNIT 1 : PRECALCULUS PREP

 LESSON 1: REAL NUMBERS, OPEN & CLOSED INTERVALS

 

Text Box: The Number Systems Defined:

Natural Numbers     the ordinary counting numbers.
			N = {1, 2, 3, 4, 5, 6, . . .  }

Whole Numbers      the natural numbers including the zero element.
			W = {0, 1, 2, 3, 4, 5, 6, . . .   }

Integers                   the natural numbers including their negatives and zero.
			  I = { . . . 4, -3, -2, -1, 0, 1, 2, 3, . . .}

Rational Numbers	- the set of all possible ratios of integers with non-zero denominators.  Basically this includes all fractions (positive and negative) in the form a/b as the definintion below suggests.
			      
In decimal form this would include all terminating decimals and non-terminating, repeating decimals which can be obtained from dividing out the fraction form of the rational number.

 

Irrational Numbers  these are numbers that are not rational  ie  the set of all non  terminating, non  repeating decimals.  

 
Real Numbers  the union of the rational numbers and irrational numbers is the Real number system.
 


 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Note: In these notes, we are talking about real numbers unless otherwise stated.

 

Intervals:

 

 

The interval can also be illustrated on a number line as below.

 

OR

 

NOTE: Open circles or round brackets indicate that the end point indicated is not included.

 

 

 

 

 

The interval can also be illustrated on a number line as below.

OR

 

NOTE: Closed circles or square brackets indicate that the end point indicated is included.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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