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These flashcards cover key concepts related to proof techniques, particularly proof by contradiction and proof by cases, as discussed in the notes.
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Proof by Contradiction
A proof method that assumes the negation of the statement is true, leading to a contradiction.
Contradiction
A situation where two or more statements or propositions are in conflict, leading to a logical impossibility.
Even Integer
An integer that is divisible by 2.
Multiple of 4
A number that can be expressed as 4 times an integer.
Theorem
A mathematical statement that has been proven based on previously established statements.
Proof by Cases
A method of proof where different scenarios (cases) are considered to prove a theorem.
Domain
The set of values that a variable can take.
Case 1: n > 0
A scenario considered in a proof where the integer n is greater than zero.
Case 2: n < 0
A scenario considered in a proof where the integer n is less than zero.
Case 3: n = 0
A scenario considered in a proof where the integer n is equal to zero.
Real Number
Any number that can be found on the number line, including both rational and irrational numbers.
Absolute Value
The non-negative value of a number without regard to its sign.
Assumption
A statement accepted as true for the purpose of argument or investigation.
Contradictory statement
A statement that opposes another statement making it impossible for both to be true.