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Proof by Contradiction
course Algorithmics
last review @April 4, 2023
mastery rookie
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Proof by Contradiction
Definition
Proof by contradiction is a method of proof that involves assuming that a statement
is false and then demonstrating that this assumption leads to a contradiction. This
contradiction must be something that is clearly false or nonsensical.
Purpose
Proof by contradiction is often used when the direct proof is difficult or impossible. By
assuming the opposite of what is to be proven and then demonstrating that it leads
to a contradiction, one can indirectly prove the original statement to be true.
Example
Suppose we want to prove that the square root of 2 is irrational. We start by
assuming, for the sake of contradiction, that the square root of 2 is a rational
Proof by Contradiction 1
Proof by Contradiction
course Algorithmics
last review @April 4, 2023
mastery rookie
assignment
progress not started
Weight
Files Proof by Contradiction.pptx
date
due date
notes
days left
Proof by Contradiction
Definition
Proof by contradiction is a method of proof that involves assuming that a statement
is false and then demonstrating that this assumption leads to a contradiction. This
contradiction must be something that is clearly false or nonsensical.
Purpose
Proof by contradiction is often used when the direct proof is difficult or impossible. By
assuming the opposite of what is to be proven and then demonstrating that it leads
to a contradiction, one can indirectly prove the original statement to be true.
Example
Suppose we want to prove that the square root of 2 is irrational. We start by
assuming, for the sake of contradiction, that the square root of 2 is a rational
Proof by Contradiction 1
