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The paradoxes do not arise with classes because there is no notion of classes containing classes. Otherwise, one could, for example, define a class of all classes that do not contain themselves, which would lead to a Russell paradox for classes. A conglomerate, on the other hand, can have proper classes as members. [2]
This page will attempt to list examples in mathematics. To qualify for inclusion, an article should be about a mathematical object with a fair amount of concreteness. Usually a definition of an abstract concept, a theorem, or a proof would not be an "example" as the term should be understood here (an elegant proof of an isolated but particularly striking fact, as opposed to a proof of a ...
In mathematics education, a representation is a way of encoding an idea or a relationship, and can be both internal (e.g., mental construct) and external (e.g., graph). Thus multiple representations are ways to symbolize, to describe and to refer to the same mathematical entity. They are used to understand, to develop, and to communicate ...
The language of mathematics or mathematical language is an extension of the natural language (for example English) that is used in mathematics and in science for expressing results (scientific laws, theorems, proofs, logical deductions, etc.) with concision, precision and unambiguity.
For example, the prime number theorem — originally proved using techniques of complex analysis — was once thought to be a deep result until elementary proofs were found. [1] On the other hand, the fact that π is irrational is usually known to be a deep result, because it requires a considerable development of real analysis before the proof ...
A valid number sentence that is true: 83 + 19 = 102. A valid number sentence that is false: 1 + 1 = 3. A valid number sentence using a 'less than' symbol: 3 + 6 < 10. A valid number sentence using a 'more than' symbol: 3 + 9 > 11. An example from a lesson plan: [6] Some students will use a direct computational approach.
AC – Axiom of Choice, [1] or set of absolutely continuous functions. a.c. – absolutely continuous. acrd – inverse chord function. ad – adjoint representation (or adjoint action) of a Lie group. adj – adjugate of a matrix. a.e. – almost everywhere. AFSOC - Assume for the sake of contradiction; Ai – Airy function. AL – Action limit.
Various sentences using the syllables mā, má, mǎ, mà, and ma are often used to illustrate the importance of tones to foreign learners. One example: Chinese: 妈妈骑马马慢妈妈骂马; pinyin: māma qí mǎ, mǎ màn, māma mà mǎ; lit. 'Mother is riding a horse... the horse is slow... mother scolds the horse'. [37]