contradiction
proof by contradiction
It is a type of indirect proof: more specifically, a proof by contradiction.
False
Another name for an indirect proof is a "proof by contradiction." In this method, one assumes the opposite of what is to be proved, leading to a logical contradiction, thereby establishing the truth of the original statement. This technique is commonly used in mathematics and logic to demonstrate the validity of propositions.
The goal of a proof by contradiction is to establish the truth of a statement by assuming the opposite is true and then demonstrating that this assumption leads to a logical contradiction. By showing that the assumption cannot hold, the original statement is validated. This technique is particularly effective in cases where direct proof is challenging. Ultimately, it reinforces the validity of the proposition by revealing inconsistencies in its negation.
Proof by contradiction is also known by its Latin equivalent, reductio ad absurdum.
contradiction
contradiction
An indirect proof is a proof by contradiction.
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To demonstrate the validity of a statement using proof by absurdity or contradiction, we assume the opposite of the statement is true and then show that this assumption leads to a logical contradiction or absurdity. This contradiction proves that the original statement must be true.
proof by contradiction
Proof by contradiction (APEX)
It is a type of indirect proof: more specifically, a proof by contradiction.
TrueIt is true that the body of an indirect proof you must show that the assumption leads to a contradiction. In math a proof is a deductive argument for a mathematical statement.
TrueIt is true that the body of an indirect proof you must show that the assumption leads to a contradiction. In math a proof is a deductive argument for a mathematical statement.