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The language of mathematics has a wide vocabulary of specialist and technical terms. It also has a certain amount of jargon: commonly used phrases which are part of the culture of mathematics, rather than of the subject.
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: "All humans are mortal, and Socrates is a human. ∴ Socrates is mortal." ∵ Abbreviation of "because" or "since". Placed between two assertions, it means that the first one is implied by the second one. For example: "11 is prime ∵ it has no positive integer factors other than itself and one." ∋ 1. Abbreviation of "such that".
When G is d-regular, meaning each vertex is of degree d, there is a relationship between the isoperimetric constant h(G) and the gap d − λ 2 in the spectrum of the adjacency operator of G. By standard spectral graph theory, the trivial eigenvalue of the adjacency operator of a d-regular graph is λ 1 = d and the first non-trivial eigenvalue ...
In mathematics, a structure on a set (or on some sets) refers to providing it (or them) with certain additional features (e.g. an operation, relation, metric, or topology). Τhe additional features are attached or related to the set (or to the sets), so as to provide it (or them) with some additional meaning or significance.
pdf – probability density function. pf – proof. PGL – projective general linear group. Pin – pin group. pmf – probability mass function. Pn – previous number. Pr – probability of an event. (See Probability theory. Also written as P or.) probit – probit function. PRNG – pseudorandom number generator.
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Delphi and D implement dynamic arrays at the language's core. Ada's Ada.Containers.Vectors generic package provides dynamic array implementation for a given subtype. Many scripting languages such as Perl and Ruby offer dynamic arrays as a built-in primitive data type.