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22 Cards in this Set
- Front
- Back
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What are whole numbers?
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1,2,3,4 ...
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what are digits?
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0-9
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what are natural #s?
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1,2,3,4...
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what are intigers?
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whole numbers andt heir opposites
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what is a Rational #?
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a number taht can be expressed as a simple fraction (no decimals or radicals in fraction), repeating decimals and terminating decimals
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what are irrational numbers?
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decimals that do not end or repeat (like pie) and cannot be expressed as a ratio of two integers
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what are transcendental #s?
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a # that cannot be expressed exactly by performing a number of algebraic operations on integers (such as pie)
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what are real numbers
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real numbers, rational numbers, transcendental numbers
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what are imaginary #s?
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square roots of negative numbers
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what is the complex# system
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real numbers and imaginary numbers
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closure axiom
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the set of all real numbers is closed under + and x. if X and Y are real numbers: X+Y and (XxY) = a real # (ur answer is a number of ur original set)
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Communitativity Axiom
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X+Y=Y+X
X*Y=Y*X |
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Associativity Axiom
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(x+y)+z = x+(y+z)
(xy)*z = x*(yz) |
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Distributive Axiom
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x(y+z) = xy+xz
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Identity Elements
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Additive element = 0
Multiplicitive element = 1 |
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Inverses
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additive invers of x=(-x)
multiplicitive inverse of x=(1/x) |
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Field
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a set that obeys all axioms
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Domain
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where values of variables come from
assumed to be the set of real #s unless otherwise specified |
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polynomials
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algebraic expressions that involve only the operations of addition, mult. and sub. on variables
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terms
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in an expression are the parts of the expression taht are connected by addition or subtraction
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Extraneous Roots
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when u transform an equasion you end upp with a solution that does not satisfy the original equasion
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Irreversible steps
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x and/or ÷ both sides an equasion by something other than 0 can serult in extra solution or loss of solution
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