indirect proof

[/ɪnˈdɪrekt pruːf/]
nounpl: indirect proofs
prova indireta
1. A method of mathematical or logical proof in which one assumes the negation of the statement to be proven and derives a contradiction, thereby establishing the truth of the original statement
The mathematician used an indirect proof to demonstrate that the square root of 2 is irrational by assuming it was rational and reaching a contradiction.
O matemático usou uma prova indireta para demonstrar que a raiz quadrada de 2 é irracional, assumindo que era racional e chegando a uma contradição.
2. Also known as proof by contradiction or reductio ad absurdum; a logical technique where the opposite of what needs to be proven is assumed true until an impossibility emerges
In the indirect proof of this theorem, we assume the opposite conclusion and work backwards.
Na prova indireta deste teorema, assumimos a conclusão oposta e trabalhamos de trás para frente.
Indirect proof is a fundamental technique in formal mathematics and logic education in both Brazil and the United States. It is particularly emphasized in discrete mathematics, geometry, and proof-based courses. This method reflects the logical traditions in mathematical pedagogy across both countries and is considered an essential problem-solving strategy in academic mathematics.
Synonyms / Sinônimos
proof by contradictionreductio ad absurdumproof by contrapositiveindirect reasoning
Antonyms / Antônimos
direct proofconstructive proof

Regional Variations

General Brazilian
prova indireta
Standard mathematical terminology used in Brazilian universities and textbooks
São Paulo
prova indireta
Used consistently in academic mathematical contexts
Portugal
prova indireta
Also used in Portuguese mathematics; sometimes called 'demonstração indireta' or 'redução ao absurdo'

Related Words

contrapositivecontradictionlogical reasoningmathematical proofassumptionnegation

Related Idioms & Phrases

proof by contradiction
reduce to absurdity
assume the opposite
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