LAP 1: Real Numbers Vocabulary
element of
a member in a set.
Order Symbols
( ), brackets, +, -, × or ⋅, ÷ or /, and =.
Integers
-3, -2, -1, 0, 1, 2, 3 -negative and positive whole numbers(no fractions and no decimals)
Rational Numbers
-3, -2.5, -2, -1.5, -1, 0 1, 1 3/2 a number that can be within the form p/q where p and q are integers and q cannot equal zero(includes fractions and decimals)(Can have repeating decimals)(Can have terminating decimals).
Whole Numbers
0, 1, 2, 3, 4, 5, 6 -natural numbers and zero(no fractions, no decimals, and no negative numbers)
Natural Numbers
1, 2, 3, 4, 5, 6 -counting numbers(no zero, no fractions, and no decimals)(no negative numbers)
Irrational Numbers
3.14... -non-repeating and non-terminating decimals(numbers that CANNOT be expressed as a fraction).
Property of the Opposite of a Sum
For all real numbers a and b, -(a+b)= (-a) + (-b).
Multiplicative Property of Zero
For every real number a, a ⋅ 0= 0 and 0 ⋅ a= 0.
Multiplicative Property of -1
For every real number a, a(-1)= -a and (-1)a= -a.
Order of Operations
PEMDAS: P= Parentheses, E= Exponent, M= Multiplication, D= Division, A= Addition, and S= Subtraction.
Terminating Decimal
a decimal that ends.
Repeating Decimal
a decimal that repeats.
Power
a number that indicates the operation of repeated multiplication.
Base
a number that is used as a repeated factor.
Finite Set
a set in which the number of elements is limited.
Infinite Set
a set in which the number of elements is unlimited.
Subset
a set that forms part of another given set.
Set
a well-defined group of objects.
Operation
addition, subtraction, multiplication, and division are the basic arithmetic operations.
Arithmetic Operation
addition, subtraction, multiplication, and division.
Numerical Expression
an expression that names a particular number; a numeral.
Number
any of the following counts(get the joke?) as a number: real numbers, natural numbers, whole numbers, integers, rational numbers, and irrational numbers.
Real Numbers
are any numbers that are either positive, negative, or zero.
Negative Numbers
are numbers to the left of zero.
Positive Numbers
are numbers to the right of zero.
Intersection
for any two sets a and b, the set consisting of these members and only these members can be common to a and b.
Union
for any two sets a and b, the set whose numbers belong to at least one of the sets a and b.
Exponent
in a power, the number that indicates how many times the base is used as a factor.
Terms
in the sum a+b, a and b are called terms.
Number Line
is a visual rpresentation of the set of real numbers.
Unit Distance
is the distance between two points on a number line.
Simplify
reducing to the lowest terms possible.
Equal Set
sets with precisely the same elements.
Inequality Symbols
symbols used to show the order of two real numbers. The symbol =/=(an equal sign with a slash through it) means "is not equal to."
Value of a Numerical Expression
the number named by the expression.
Coordinate
the number paired with a point. Number to letter.
Reciprocal
the number which, when multiplied times a particular fraction, gives the result of 1.
Definition of Subtraction
the operation of finding a difference or process of taking away one number from other to find the quantity left; represented by the symbol -.
Origin
the origin is zero and it is also known as the middle of the number line.
Graph
the point paired with a number on a number line. Letter to number.
Absolute Value
the positive number of any pair of opposite non-zero real numbers is the absolute value of each number. The absolute value of 0 is 0. The absolute value of a number is denoted by lal.
Definition of Division
the process of calculating how many times one quantity is contained in another; represented by the symbol (image division symbol) or /.
Opposites
two numbers that lie the same distance from 0 on the number line, but in opposite directions.
Disjoint
two sets that have no members in common.
Factors
when two or more numbers are multiplied, each of the numbers is a factor of the product.
