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A fact is a true datum about one or more aspects of a circumstance. [1] Standard reference works are often used to check facts. Scientific facts are verified by repeatable careful observation or measurement by experiments or other means. For example, "This sentence contains words."
A central aspect concerns the abilities used to distinguish facts from mere opinions, like the process of finding and evaluating reasons for and against a position to come to one's own conclusion. [114] This includes being able to differentiate between reliable and unreliable sources of information.
In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. [1] [2] [3] Some conjectures, such as the Riemann hypothesis or Fermat's conjecture (now a theorem, proven in 1995 by Andrew Wiles), have shaped much of mathematical history as new areas of mathematics are developed in order to ...
Story at a glance Knowing the difference between fact and opinion seems simple, but respondents in a survey published earlier this month were largely unable to correctly identify either. Two ...
The definition of a formal proof is intended to capture the concept of proofs as written in the practice of mathematics. The soundness of this definition amounts to the belief that a published proof can, in principle, be converted into a formal proof. However, outside the field of automated proof assistants, this is rarely done in practice.
The fact–value distinction is also closely related to the moralistic fallacy, an invalid inference of factual conclusions from purely evaluative premises. For example, an invalid inference "Because everybody ought to be equal, there are no innate genetic differences between people" is an instance of the moralistic fallacy.
A "judicial opinion" or "opinion of the court" is an opinion of a judge or group of judges that accompanies and explains an order or ruling in a controversy before the court. A judicial opinion generally lays out the facts that the court recognized as being established, the legal principles the court is bound by, and the application of the ...
In mathematics, certain kinds of mistaken proof are often exhibited, and sometimes collected, as illustrations of a concept called mathematical fallacy.There is a distinction between a simple mistake and a mathematical fallacy in a proof, in that a mistake in a proof leads to an invalid proof while in the best-known examples of mathematical fallacies there is some element of concealment or ...