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In logic a counterexample disproves the generalization, and does so rigorously in the fields of mathematics and philosophy. [1] For example, the fact that "student John Smith is not lazy" is a counterexample to the generalization "students are lazy", and both a counterexample to, and disproof of, the universal quantification "all students are ...
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For instance, an example of a first-countable space which is not second-countable is counterexample #3, the discrete topology on an uncountable set. This particular counterexample shows that second-countability does not follow from first-countability. Several other "Counterexamples in ..." books and papers have followed, with similar motivations.
See as example Category:English words. Language portal; Subcategories. This category has only the following subcategory. ... Pages in category "Hindi words and phrases"
However, the failure to find a counterexample after extensive search does not constitute a proof that the conjecture is true—because the conjecture might be false but with a very large minimal counterexample. Nevertheless, mathematicians often regard a conjecture as strongly supported by evidence even though not yet proved.
This is a list of English-language words of Hindi and Urdu origin, two distinguished registers of the Hindustani language (Hindi-Urdu). Many of the Hindi and Urdu equivalents have originated from Sanskrit; see List of English words of Sanskrit origin.
Hindustani, the lingua franca of Northern India and Pakistan, has two standardised registers: Hindi and Urdu.Grammatical differences between the two standards are minor but each uses its own script: Hindi uses Devanagari while Urdu uses an extended form of the Perso-Arabic script, typically in the Nastaʿlīq style.
The Gettier problem, in the field of epistemology, is a landmark philosophical problem concerning the understanding of descriptive knowledge.Attributed to American philosopher Edmund Gettier, Gettier-type counterexamples (called "Gettier-cases") challenge the long-held justified true belief (JTB) account of knowledge.