number line
numbers can be placed in correspondence with points on a line
origin
the point corresponds to the number zero; the place where something begins
positive number
a number that corresponds to a point on th episitive side of a number line
negative number
a number that corresponds to a point on the negative side of the number line
graph on the number
on a number line the point that correspoinds to a number
real number
any number that is either a positive number, a negative number or zero
directed numbers
positive and negative numbers suggest opposite directions
equal set
sets that contain exactly the same members
one-to-one correspondence
Although the set are not equal, there is an important relations between them
roster
list all the members of a set
rule
specify a set by writing within the braces a description that identifies the members of the set; example: {1, 3, 5, 7,} = {the odd numbers between 0 and 8}
graph of set
graph the numbers on a line; set of points corresponding to a set of numbers
subset
if every member of a set S is also a member of set T, then S is a subset of T; symbol C;
empty set or null set
set contains no members
Venn diagram
diagram showing how certain sets are related
natural numbers or counting numbers
set of numbers used in counting; symbol N
whole numbers
expand the set of natural numbers to include the number 0; symbol W
integers
All whole numbers (both positive and negative) and zero; pattern continues without end in both directions; symbol J
rational numbers
any number that can be expressed as the quotient of tow integers, provided the divisor is not 0; exxample: 0= 0/1, 7=7/1, .21=21/100; symbol Q
irrational numbers
numbers that cannot be expressed as the quotient of two integers; symbols R
infinite set
each of the sets N (Natural numbers), W (Whole numbers), J (integers), Q (Rational Numbers ), R (Irrational numbers)
finite set
a set that is not ian nfinite set
numerical expression or numeral
a name for a number; example: 4 x 9 = 36
simplify the expression
a numerical expression with the simplest or most common name; example: 36 vs. 4 x 9 -=36
substitution principle
changing the numeral by which a number is named in an expression does not change the value of the expression
variable
symbol used to represent one or more numbers
domain or replacement set
set of numbers that a variable may represent
value of the variable
each number in the domain
variable expression
contains one or more variables and also may contain other symbols
evaluate the expression or find the value of the expression
when you replace each variable in a variable expression with one of its values and simplify the resulting numerical expression
mathematical expression
a numerical express or a variable expression
grouping symbol
is a device, such as a pair of parentheses, that is used to enclose an expression; braches, [ ] or braces { }
base
in an expression like 3 x 3 x 3 x 3 x 3 = 3 to the 5th power; the base is 3
exponent
in a power, the number of times the base occurs as a factor; example: 3 x 3 x 3 x 3 x 3 = 3 to the 5th power; the exponent is 5
exponential form
3 to the fifth power is noted as expontential form
order of operations
1. first simplify expressions within grouping symbols
2. then simplify powers
3. then, simplify products and quotients in order form left to right
4. then simplify sums and differences in order from left to right
mathematical sentence
a statement that indicates a relationship between two mathematcial expressions
equation
if a mathematical sentence states that two expressions name the same number; the equal sign, =
sides of equation
two expressions; example; 4 x 7 = 28; 4 x 7 is the left side of the equation and 28 is the right side
sides of the inequality
the expressions to the left and right of an inequality symbol
open mathematical sentence or open sentence
a mathematical sentence that contains at least one variable; example: 2x - 5 = 35
solution or root
any value of the variables for which the open sentence is true
solution set
the set of all solutions of the system
satisfy
each member of the solution set of an open sentence is said to satisfy the open sentence
graph of an open sentence
is the graph of its solution set
set-builder notation
the set of all "x" such that "x" is greater than 1