# Shared Flashcard Set

## Details

The Real Number System
Basic Concepts of Algebra
26
Mathematics
03/18/2008

Term
 Rational Numbers
Definition
 Numbers that can be expressed in the form p/q, where p and q are integers and q ≠ 0.  Decimal notation for rational numbers either terminates or repeats.
Term
 Irrational Numbers
Definition
 The real numbers that are not rational numbers.  Decimal notation for irrational numbers neither terminates nor repeats.
Term
 Real Numbers
Definition
 The set of all rational numbers combined with the set of all irrational numbers.  Real numbers are modeled using a number line.
Term
 element
Definition
 A member belonging to a set.
Term
 subset
Definition
 When all the elements of one set are elements of a second set, the first set is a subset of the second set.
Term
 Interval Notation
Definition
 Open          (a,b)            {x | a < x < b}Closed        [a,b]               {x | a ≤ x ≤ b}Half-open   [a,b)               {x | a ≤ x < b}Half-open   (a,b]               {x | a < x ≤ b}Open          (a,∞)              {x | x > a}Half-open   [a,∞)              {x | x ≥ a}Open          (-∞,b)            {x | x < b}Half-open   (-∞,b]             {x | x ≤ b}
Term
 Commutative Properties of Addition and Multiplication
Definition
 a + b = b + aab = ba
Term
Definition
 a + (b + c) = (a + b) + ca(bc) = (ab)c
Term
Definition
 a + 0 = 0 + a = a
Term
Definition
 -a + a = a + (-a) = 0
Term
 Multiplicative Identity Property
Definition
 a · 1 = 1 · a = a
Term
 Multiplicative Inverse Property
Definition
 a · 1/a = 1/a · a = 1  (a ≠ 0)
Term
 Distributive Property
Definition
 a(b + c) = ab + ac
Term
 Absolute Value
Definition
 |a| = a if a ≥ 0|a| = -a if a < 0
Term
 Distance Between Two Pointson the Number Line
Definition
 For any real numbers a and b, the distance between a and b is |a - b| or equivalently, |b - a|.
Term
 Absolute Value of a Product
Definition
 For any real numbers a and b and any nonzero number c:   |ab| = |a| · |b|.
Term
 Absolute Value of a Quotient
Definition
 For any real numbers a and b and any nonzero number c:  |a/c| = |a| / |c|.
Term
 Absolute Value of an Exponent
Definition
 For any real numbers a and b and any nonzero number c:  |an| = an if n is an even integer.
Term
 Absolute Value of Negative and Positive Numbers
Definition
 For any real numbers a and b and any nonzero number c:  |-a| = |a|.
Term
 Multiplying by -1
Definition
 For any real number a, -1 · a = -a (Multiplying a number by -1 produces its opposite.)
Term
 Opposites
Definition
 For any real number a, - (-a) = a (The opposite of the opposite of a number is the number itself.)
Term
Definition
 Positive numbers: Add the numbers.  The result is positive.Negative numbers: Add the absolute values.  Make the answer negative.A positive and a negative number: Subtract the smaller absolute value from the larger.  Then:If the positive number is the greater absolute value, make the answer positive.If the negative number has the greater absolute value, make the answer negative.If the numbers have the same absolute value, make the answer 0.One number is zero: The sum is the other number.
Term
 Natural Numbers
Definition
 Those numbers used for counting {1, 2, 3, . . . }
Term
 Whole Numbers
Definition
 The natural numbers and 0 {0, 1, 2, 3, . . . }
Term
 Integers
Definition
 The whole numbers and their opposites{. . . -3, -2, -1, 0, 1, 2, 3, . . .}.
Term
 roster method
Definition
 A method of denoting sets.e.g., a set containing the numbers 2, 3, 4, and 5 can be written using the roster method: {2, 3, 4, 5}.
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