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Rigour (British English) or rigor (American English; see spelling differences) describes a condition of stiffness or strictness. [1] These constraints may be environmentally imposed, such as "the rigours of famine"; logically imposed, such as mathematical proofs which must maintain consistent answers; or socially imposed, such as the process of defining ethics and law.
The standard of rigor is not absolute and has varied throughout history. A proof can be presented differently depending on the intended audience. To gain acceptance, a proof has to meet communal standards of rigor; an argument considered vague or incomplete may be rejected. The concept of proof is formalized in the field of mathematical logic. [12]
Pragmatic validity in research looks to a different paradigms from more traditional, (post)positivistic research approaches. It tries to ameliorate problems associated with the rigour-relevance debate, and is applicable in all kinds of research streams.
In a context not requiring rigor, this phrase often appears as a labor-saving device when the technical details of a complete argument would outweigh the conceptual benefits. The author gives a proof in a simple enough case that the computations are reasonable, and then indicates that "in general" the proof is similar. index battle
This category includes articles on basic topics related to mathematical proofs, including terminology and proof techniques. Related categories: Pages which contain only proofs (of claims made in other articles) should be placed in the subcategory Category:Article proofs .
Pennsylvania’s Punxsutawney Phil might be the most well-known weather-predicting groundhog, but a new list casts doubt on his accuracy.Phil did so poorly that even nonliving critters outshine ...
What happens after an executive order is signed? After a president signs an executive order, the White House sends the document to the Office of the Federal Register, the executive branch's ...
The first complete proof was given by Hilbert in 1896. In 1879, Alfred Kempe published a purported proof of the four color theorem, whose validity as a proof was accepted for eleven years before it was refuted by Percy Heawood. Peter Guthrie Tait gave another incorrect proof in 1880 which was shown to be incorrect by Julius Petersen in 1891.