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| An integer is called EVEN provided it is divisible by two. |
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| Let a and b be integers. We say that a is DIVISIBLE by b provided there is an integer c such that bc = a. b|a |
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| An integer a is called ODD provided there is an integers x such that a = 2x + 1. |
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| An integer p is called PRIME provided that p > 1 and the only positive divisors of p are 1 and p. |
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| A positive integer a is called COMPOSITE provided that there is an integer b such that 1 < b < a and b|a. |
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| When statements in the for "If A, then B" in which condition A is impossible, but are considered true because they have no exceptions. |
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| A modest, generic word for a theorem. |
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| A minor theorem. More important or more general than a fact. |
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| A theorem whose main purpose is to help prove another more important theorem. |
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| A result with a short proof whose main step is the use of another, previously proved theorem. |
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| A claim is a theorem whose statement usually appears inside the proof of a theorem . The purpose is to help organize key steps in a proof. Similar to lemma. |
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| Every even integer greater tan two is the sum of two primes. |
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| The typical way to disprove an if-then statement. "If A, then B", Find where A is true but B is false. |
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| A variable that takes on only two possible values: true or false. |
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| A Boolean expression whose value is true for all possible values of the variables in the expression. ex. A or notA |
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| Two Boolean expressions are logically equivalent if they are equal for all possible values of their variables. |
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| An ordered sequence of objects. Can include something twice. Elements separated by commas. Surrounded by parenthesis. Elements can be anything. |
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| The number of elements a list contains. |
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| They have the same length and elements in corresponding positions are equal. |
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| Lists of length k, each element selected from n possible objects (repetition allowed). |
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| Lists of length k, each element selected form n possoble objects (no repetition allowed). n(n-1)(n-2)..(n-k+1) |
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Same backwards and forwards.
example: HANNAH |
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| An unordered, repetition free collection of objects. Comma separated elements surrounded by curly brackets. {a,b,c} |
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| The length or umber of elements in a set. |A| |
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| A set containing exactly one element. {a} |
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| A = B when they contain exactly the same elements. |
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| An object that belongs to a set. |
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| {dummy variable : conditions} |
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| Suppose A and B are sets. We say that A is a SUBSET of B provided every elements of A is also an element of B. |
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| We say A is a PROPER SUBSET of B, denoted A c B, provided A is a subset of B and A does not equal B. |
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| Let A be a set. The POWER SET of A is the set of all the subsets of A. 2^A. |
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| Cardinality of a Power Set |
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|2^A| = 2^|A|
(2 to the power of the cardinality of A. |
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| upside down A. read FOR ALL. |
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| backwards E. read THERE EXISTS. |
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