Lecture 11 - Proofs (Part 3)

These flashcards cover key concepts related to proof techniques, particularly proof by contradiction and proof by cases, as discussed in the notes.

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.