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Ending a proof
Main article: Q.E.D.Sometimes, the abbreviation "Q.E.D." is written to indicate the end of a proof. This abbreviation stands for "Quod Erat Demonstrandum", which is Latin for "that which was to be dem ...
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Related concepts
Visual proof Although not a formal proof, a visual demonstration of a mathematical theorem is sometimes called a "proof without words". The left-hand picture below is an example of a historic visual p ...
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Heuristic mathematics and experimental mathematics
Main article: Experimental mathematicsWhile early mathematicians such as Eudoxus of Cnidus did not use proofs, from Euclid to the foundational mathematics developments of the late 19th and 20th centur ...
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Undecidable statements
A statement that is neither provable nor disprovable from a set of axioms is called undecidable (from those axioms). One example is the parallel postulate, which is neither provable nor refutable from ...
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Methods of proof
Direct proof Main article: Direct proofIn direct proof, the conclusion is established by logically combining the axioms, definitions, and earlier theorems. For example, direct proof can be used to est ...
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Nature and purpose
As practised, a proof is expressed in natural language and is a rigorous argument intended to convince the audience of the truth of a statement. The standard of rigor is not absolute and has varied th ...
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History and etymology
The word "proof" comes from the Latin probare meaning "to test". Related modern words are the English "probe", "probation", and "probability", the Spanish probar (to smell or taste, or (lesser use) to ...
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Mathematical proof
In mathematics, a proof is a deductive argument for a mathematical statement. In the argument, other previously established statements, such as theorems, can be used. In principle, a proof can be trac ...
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Relation to randomness
In a deterministic universe, based on Newtonian concepts, there would be no probability if all conditions were known (Laplace's demon), (but there are situations in which sensitivity to initial condit ...
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Mathematical treatment
Consider an experiment that can produce a number of results. The collection of all results is called the sample space of the experiment. The power set of the sample space is formed by considering all ...
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Applications
Probability theory is applied in everyday life in risk assessment and in trade on financial markets. Governments apply probabilistic methods in environmental regulation, where it is called pathway ana ...
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Theory
Main article: Probability theoryLike other theories, the theory of probability is a representation of probabilistic concepts in formal terms—that is, in terms that can be considered separately from t ...
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History
Main article: History of probabilityThe scientific study of probability is a modern development. Gambling shows that there has been an interest in quantifying the ideas of probability for millennia, b ...
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Etymology
The word Probability derives from the Latin probabilitas, which can also mean probity, a measure of the authority of a witness in a legal case in Europe, and often correlated with the witness's nobili ...
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Interpretations
Main article: Probability interpretationsWhen dealing with experiments that are random and well-defined in a purely theoretical setting (like tossing a fair coin), probabilities describe the statistic ...
category:    2014-3-24 21:09

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