proof by contradiction
/ˌpruːf baɪ ˌkɒntrəˈdɪkʃən/
proving a statement by showing its negation leads to an impossibility
proof by contradiction in a sentence
“The irrationality of √2 is elegantly shown by proof by contradiction.”
Origin of proof by contradiction
From Latin contradicere to speak against
Related Words
induction
proving a statement for all natural numbers by establishing a base case and inductive step
axiom
a statement accepted as true without proof, serving as a starting point for reasoning
theorem
a statement that has been proven true based on axioms and other theorems
lemma
a proven proposition used as a stepping stone to a larger result
corollary
a proposition that follows directly from a proven theorem
conjecture
a proposition believed to be true but not yet proven