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| connected series of statements to establish a definite proposition |
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| a variable that is quantified |
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| x two sets A and B is the set of all ordered pairs of (a,b) such that a member B b member A |
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| Combination of multiple propositions. |
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| Proposition that is neither a tautology or a contradiction |
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| Proposition that always evaluates to false |
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| Theorem who's truth follows directly from an accepted theorem |
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| Moves from accepted general principals to specific situation. |
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| encompasses the representation and study of collections of distinct objects |
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| Intersection is the empty set |
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| A collection of values from which a variable's value is drawn |
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| Argument constructed with improper inference. |
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| Largest integer such that i|x and i|y |
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| Disjunction of predicates in which at most one of the predicates is not negated |
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| In is a nxn with ones down main diagonal |
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| Moves from specific observations to a general conclusion. |
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| smallest integer such that x|s and y|s |
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| simple theorem whose truth is used to construct more complex theorems |
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| Both propositions evaluate to the same result when presented with the same input |
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| The use of formal languages and grammars to represent the syntax and semantics of computation. |
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| S steps with n1 ways first n2 second etc. then n1*n2...ns ways to complete |
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| Set of two items (a,b) (a,b) not equal (b,a) unless a=b |
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| Separates its members into disjoint sets |
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| The classical notion of 'logic' The study of thought and reasoning. |
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| n items in k boxes then one box has ceiling (n/k) items |
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| Set of all of A's subset including empty set. |
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| A statement that includes one or more variables and will evaluate to either true or false when the variables are assigned values |
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| sound argument that establishes the truth of a theorem |
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| is a claim that is either true or false with respect to an associated context |
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| Ordered range of a function from a set of integers to a set S. |
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| Unordered collection of unique objects |
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| A proposition that contains no logical operators. |
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| Valid argument that has true premises |
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| Unsupported or improperly constructed argument |
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| A is a ███▐█ B if every member of A can be found in B |
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| Proposition that always evaluates to true |
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| Denoted A^T mxn = nxm rows and columns exchanged. |
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| Conclusion must follow from the hypothesis |
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| A correctly structured expression of a language. |
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| set of instructions for performing a task |
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| constant called common difference |
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| statement with unknown truth value |
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| finite or countable infinite |
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| bijective mapping is to either of the sets Z* or Z+ |
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| reflexive symmetric and transitive |
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| i and j positive integers. i %j = 0 |
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| bijective mapping between it and set of cardinality n |
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| f: X -> Y is a relation from X to Y. |
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f(n) = p
p is image
n is preimage |
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| increasing sequence (non decreasing) |
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| complex problems are handled in terms of simplier versions |
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| f(x) = y for at most one member of X |
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| irreflexive partial order |
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| reflexive, antisymmetric and transitive |
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| n-Dimensional collection of values |
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| reflexive, antisymmetric and transitive |
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| ordering of n distinct elements |
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| only factors are 1 and then number also number > 2 |
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| a is ███ B A is a subset of B and A not equal B |
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| ordering of r-elemtn subset of n distinct elements |
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| set of all images of elements of X |
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| basis, inductive and sometimes external clause |
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| strictly increasing sequence |
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| continuous finite sequence of zero or more elements of x are found within y in the same relative order. |
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| f's range is Y (range=codomain) |
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| Conjecture that is shown to be true |
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| every pair of elements a,b are comparable |
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