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| Set | a collection of items or objects. |
| Elements | the individual items or objects that are in sets |
| Union | the joining of sets into a master set. Union will not yield multiples of the same item |
| Intersection | what is common between two sets |
| Null Set | a set with no contents |
| Subset | a set, all of whose elements are also elements of the other set |
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(Counting) |
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Square roots of negative numbers. By definition,  |
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Irrational Numbers in Decimal Form: non-repeating, non-terminating
Q is used here because R is reserved for Real Numbers. Q is a logical replacement however. It stands for Quotient, which is at the heart of the Definition of the Rational Numbers.
Definition:
| Absolute Value | The distance that a number is from zero on the number line. This must always be either zero or positive. |
| Using the above definition, if we were told that the distance from an object is x units, it means that we are either x units to the left of the goal, or x units to the right of the goal. |
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| The "-" sign in front of a number or variable really does not mean "negative," it means additive inverse. Of course the additive inverse of a number can be positive. And so, the absolute value of an expression can have a "-" sign in it. |
| Order of Operations | The order in which mathematical operations must be
done.
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| Expression | A mathematical statement using numbers, variables, and operations. | ||||||||||||||||||||||||||||
| Algebraic Expression | An expression which has at least one variable in it. | ||||||||||||||||||||||||||||
| Formula | A mathematical sentence that
expresses the relationship between certain quantities.
Example: A ball has a radius of 8.3 in. Find the surface area of the ball. A: area; r: radius  |
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| Commutative property |
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| Associative property |
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| Distributive property |
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| Identity Property |
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| Inverse Property |
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| Substitution property | if  then either can be substituted
for either at any time |
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| Closure property | If two elements of a set can be combined using an operation and a third number from that same set always results | The set of integers is closed under subtraction because when you subtract 2 integers, it will always result in an integer |
| Equal Rights Amendment for Algebra (ERAA) | Whatever you do to one side of an equation, you must do the same to the other side also. |
| Reflexive Property | For any real number a, a = a |
| Symmetric Property | For all real numbers a and b, if a = b, then b = a |
| Transitive Property | For all real numbers a, b, and c, if a = b and b = c, then a = c. |
| Property | Definition | Example | Notes |
| Equal Rights Amendment for Algebra (ERA) | Whatever you do to one side of an equation, you must do the same to the other side also |
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Subtraced 3 from both sides |
| Equal Rights Amendment for Algebra (ERA) | Whatever you do to one side of an equation, you must do the same to the other side also |
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Divided both sides by 14 |
| Equal Rights Amendment for Algebra (ERA) | Whatever you do to one side of an equation, you must do the same to the other side also |
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Multiplied both sides by 3 |
| Equal Rights Amendment for Algebra (ERA) | Whatever you do to one side of an equation, you must do the same to the other side also |
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Took both square roots of both sides |
| Equal Rights Amendment for Algebra (ERA) | Whatever you do to one side of an equation, you must do the same to the other side also |
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Squared both sides |
