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Rigor is a cornerstone quality of mathematics, and can play an important role in preventing mathematics from degenerating into fallacies. well-behaved An object is well-behaved (in contrast with being Pathological ) if it satisfies certain prevailing regularity properties, or if it conforms to mathematical intuition (even though intuition can ...
The English language has a number of words that denote specific or approximate quantities that are themselves not numbers. [1] Along with numerals, and special-purpose words like some, any, much, more, every, and all, they are quantifiers. Quantifiers are a kind of determiner and occur in many constructions with other determiners, like articles ...
Catalan castellers collaborate, working together with a shared goal. Collaboration (from Latin com-"with" + laborare "to labor", "to work") is the process of two or more people, entities or organizations working together to complete a task or achieve a goal. [1]
In mathematics, a duality, generally speaking, translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one-to-one fashion, often (but not always) by means of an involution operation: if the dual of A is B, then the dual of B is A. Alexander duality; Alvis–Curtis duality; Artin–Verdier duality
Latin and Greek letters are used in mathematics, science, engineering, and other areas where mathematical notation is used as symbols for constants, special functions, and also conventionally for variables representing certain quantities.
Visual proof of the Pythagorean identity: for any angle , the point (,) = (, ) lies on the unit circle, which satisfies the equation + =.Thus, + =. In mathematics, an identity is an equality relating one mathematical expression A to another mathematical expression B, such that A and B (which might contain some variables) produce the same value for all values of the variables ...
Alternatively—since the previous result can be unaesthetic, especially for inlined formulae presented as an image whose baseline does not line up with that of the running text—the punctuation can be placed after the </math> tag and then the whole formula (including the punctuation) can be enclosed with the {} template, as in This shows that ...
Category theory is a branch of mathematics that seeks to generalize all of mathematics in terms of categories, independent of what their objects and arrows represent. Virtually every branch of modern mathematics can be described in terms of categories, and doing so often reveals deep insights and similarities between seemingly different areas ...