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Zermelo–Fraenkel set theory. In set theory, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in the early twentieth century in order to formulate a theory of sets free of paradoxes such as Russell's paradox. Today, Zermelo–Fraenkel set theory, with the ...
The most common description of the electromagnetic field uses two three-dimensional vector fields called the electric field and the magnetic field. These vector fields each have a value defined at every point of space and time and are thus often regarded as functions of the space and time coordinates. As such, they are often written as E(x, y ...
In mathematics, a modular form is a (complex) analytic function on the upper half-plane, , that satisfies: a kind of functional equation with respect to the group action of the modular group, and a growth condition. The theory of modular forms therefore belongs to complex analysis. The main importance of the theory is its connections with ...
978-0-465-03771-1. OCLC. 44045671. Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being (hereinafter WMCF) is a book by George Lakoff, a cognitive linguist, and Rafael E. Núñez, a psychologist. Published in 2000, WMCF seeks to found a cognitive science of mathematics, a theory of embodied mathematics based on ...
1⁄2 in) standard gauge. The MF 19 ( Métro Fer appel d'offres 2019; 2019 procurement rail metro) is a class of rolling stock being built for the Paris Métro. It was ordered to replace existing trains on Lines 3, 3bis, 7, 7bis, 8, 10, 12 and 13, starting in 2025. It is being built by Alstom. Lines 3bis and 7bis will use 4-car trains, an ...
Thus these properties form a strictly weaker notion of equality than set equality in ZFC. Outside of pure math, the identity of indiscernibles has attracted much controversy and criticism, especially from corpuscular philosophy and quantum mechanics. [17] This is why the properties are said to not form a complete axiomatization.
Axiom is a general-purpose computer algebra system. It has been in development since 1971 by IBM, and was originally named scratchpad. Richard Jenks originally headed it but over the years Barry Trager who then shaped the direction of the scratchpad project took over the project. It was eventually sold to the Numerical Algorithms Group (NAG ...
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