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Metamath is a formal language and an associated computer program (a proof assistant) for archiving and verifying mathematical proofs. [2] Several databases of proved theorems have been developed using Metamath covering standard results in logic, set theory, number theory, algebra, topology and analysis, among others.
It has tens of thousands of citations, being one of the most influential and cited scientific papers of all time, [6] as it gave rise to the field of information theory, with Scientific American referring to the paper as the "Magna Carta of the Information Age", [7] while the electrical engineer Robert G. Gallager called the paper a "blueprint ...
The name Nyquist–Shannon sampling theorem honours Harry Nyquist and Claude Shannon, but the theorem was also previously discovered by E. T. Whittaker (published in 1915), and Shannon cited Whittaker's paper in his work. The theorem is thus also known by the names Whittaker–Shannon sampling theorem, Whittaker–Shannon, and Whittaker ...
LaTeX (/ ˈ l ɑː t ɛ k / ⓘ LAH-tek or / ˈ l eɪ t ɛ k / LAY-tek, [2] [Note 1] often stylized as L a T e X) is a software system for typesetting documents. [3] LaTeX markup describes the content and layout of the document, as opposed to the formatted text found in WYSIWYG word processors like Google Docs, LibreOffice Writer, and Microsoft Word.
Universal approximation theorems are limit theorems: They simply state that for any and a criterion of closeness >, if there are enough neurons in a neural network, then there exists a neural network with that many neurons that does approximate to within . There is no guarantee that any finite size, say, 10000 neurons, is enough.
When the topic is a theorem, the article should provide a precise statement of the theorem. Sometimes this statement will be in the lead, for example: Lagrange's theorem, in the mathematics of group theory, states that for any finite group G, the order (number of elements) of every subgroup H of G divides the order of G.
Kawasaki's theorem (mathematics of paper folding) Kelvin's circulation theorem ; Kempf–Ness theorem (algebraic geometry) Kepler conjecture (discrete geometry) Kharitonov's theorem (control theory) Khinchin's theorem (probability) Killing–Hopf theorem (Riemannian geometry) Kinoshita–Lee–Nauenberg theorem (quantum field theory)
In AMS-LaTeX, the symbol is automatically appended at the end of a proof environment \begin{proof}... \end{proof} . It can also be obtained from the commands \qedsymbol , \qedhere or \qed (the latter causes the symbol to be right aligned).