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counterexample
Wiktionary
counterexample

n. (context logic English) An exception to a proposed general rule; a specific instance of the falsity of a universally quantified statement.

WordNet
counterexample

n. refutation by example

Wikipedia
Counterexample

In logic, and especially in its applications to mathematics and philosophy, a counterexample is an exception to a proposed general rule or law. For example, consider the proposition "all students are lazy". Because this statement makes the claim that a certain property (laziness) holds for all students, even a single example of a diligent student will prove it false. Thus, any hard-working student is a counterexample to "all students are lazy". More precisely, a counterexample is a specific instance of the falsity of a universal quantification (a "for all" statement).

In mathematics, this term is (by a slight abuse) also sometimes used for examples illustrating the necessity of the full hypothesis of a theorem, by considering a case where a part of the hypothesis is not verified, and where one can show that the conclusion does not hold.

Usage examples of "counterexample".

So, rather than syphilis being a counterexample of the generally one-way course of epidemic disease, it confirms that the development of epidemics requires social conditions typical of overcrowded civilization.

Defense Secretary was a quiet but inpressive man, exuding a sort of iron conviction Kingsley had seldom seen, for a pointed counterexample, in the English cabinet.

Planck machine had found a counterexample, a number in the region of ten raised to the power eighty.

The counterexample is Marvin Gaye, who, when he began arranging his own material, waded even deeper into the unresolvable mire.

Any such argument claims to provide a counterexample to their general theorem, and if one such counterexample is true the general theorem must be false.

Sardonic humor flourished alongside despair, and for every personalized story of emotional exhaustion and shattered lives, it usually was possible to find an up-lifting counterexample of resilience, hope, and accomplishment.

The only counterexample in his experience was the Citadel where he grew up, which was a majestic conglomerated accumulation of centuries.

Now that Van had learned, by startling counterexamples, something about sound and competent governance, he was very aware that the Terror was just the Bubble by another name.

They had been exalted by this process, Michel saw, they were proud of their response, of how people had pulled together—also very indignant at any counterexamples of gouging or callousness, blots on an otherwise heroic affair: “Can you believe it?

They had been exalted by this process, Michel saw, they were proud of their response, of how people had pulled together-also very indignant at any counterexamples of gouging or callousness, blots on an otherwise heroic affair: "Can you believe it?

Again, that's a theory, but it's a theory supported by many thousands of cases, with no counterexamples to suggest anything different.

But you can probably come up with a dozen counterexamples to each of those descriptions without trying hard.

They collected equal numbers of counterexamples - the wonderful things that had happened, time and again, to save devout believers from catastrophe.