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the set consisting of elements that belong to A and B
Denoted A∩B
Intersection
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the set consisting of elements that belong to either A or B
denoted A∪B
Union
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The set consisting of all the elements in the universal set that are not in A
denoted ⊼ (an A with a dash above it)
Complement
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If every element of set A is also an element of a set B
denoted A⊆B
Subset
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set consisting of all elements that we wish to consider.
U
Universal Set
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a set that has no elements
denoted by the symbol ∅
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Three dots, indicate that the pattern continues indefinitely
{1,2,3,4, . . .}
ellipsis
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The set of numbers {...,-3,-2,-1,0,1,2,3, . . .}
Intigers
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a number that can be expressed as a quotient of two integers The intiger a is called the numerator , and the integer b, which cannot be 0
Rational Number
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What are natural Numbers?
{1,2,3,4, . . }
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What are Iintigers?
{. . . -3,-2,-1,0,1,2,3, . . .}
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What are Rational Numbers?
- a number that can be expressed as a quotient a/b of two intigers, Intiger a is called the numerator and the integer b, which cannot be 0 is called the denominator.
- 3/4, 5/2, 0/4, -2/3, and 100/3
rational numbers may be represented as decimals,
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what is an irrational number?
every irrational number may be represented by a decimal that neither repeats nort terminates.
Decimal
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What is a real number
The unionn of the set of rational numbers with the sset of irrational numbers.
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how do you express an approximation
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Drop all the digits that follow the specified final digit in the decimal
Truncation
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Identify the specified final digit in the decimal. If the next digit is 5 or more, add 1 to the final digit: if the next digit is 4 or less, leave the final digit as it is. then truncate following the final digit
Rounding
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"correct to a given number of decimal places"
Truncate
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+,-,*,/
sum, difference, product, quotient
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two expressions are place next to each other without an operation symbol, as in ab or in parentheses as in (a)(b) are to be multiplied
factors
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Whenever two operations of addition and multiplication seperate three numbers, which is performed first?
Multiply first, then add.
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What are the rules for Order of Operation?
- 1. begin with the innermost parentheses and work outward. Remember that in dividing two expressions, we treat the numerator and denominator as if they were enclosed in parentheses
- 2. Perform multiplications and divisions, working from left to right.
- 3. Perform additions and subtractions, working from left to right.
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states that a number equals itself: That is, a=a
Reflexive Property
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states that if a=b, then b=a
Symmetric property
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states that if a =b and b=c, then a=c
transitive property
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states that if a=b,, then we may substitute b for a in any expression containing a.
principle of substitution
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states that the order in which addition or multiplication takes place does not affect the final result
commutative properties
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the way we multiply three real numbers does not affect the final result. Expressions such as 2+3+4 and 3*4*5 present no ambiguity, even though addition and multiplication are performed on one pair of numbers at a time.
Associative Property
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