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Discontinuity (mathematics)
Continuous functions are of utmost importance in mathematics, functions and applications. However, not all functions are continuous. If a function is not continuous at a point in its domain, one says that it has a discontinuity there. The set of all points of discontinuity of a function may be a discrete set, a dense set, or even the entire domain of the function
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Jump Drive
A jump drive is a speculative method of traveling faster than light (FTL) in science fiction. Related concepts are hyperdrive, warp drive and interstellar teleporter. The key characteristic of a jump drive (as the term is usually used) is that it allows a starship to be instantaneously teleported between two points. A jump drive is supposed to make a spaceship (or any matter) go from one point in space to another point, which may be several light years away, in a single instant. Like time travel, a jump drive is often taken for granted in science fiction, but very few science fiction works talk about the mechanics behind a jump drive
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Special
Special
Special
or specials may refer to:Contents1 Music 2 Film and television 3 Other uses 4 See alsoMusic[edit] Special
Special
(album), a 1992
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Rational Point
In number theory and algebraic geometry, a rational point of an algebraic variety is a solution of a set of polynomial equations in a given field. If the field is not mentioned, the field of rational numbers may be understood. For example, (3/5, 4/5) is a rational point on the circle x2 + y2 = 1
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Indicator Function
In mathematics, an indicator function or a characteristic function is a function defined on a set X that indicates membership of an element in a subset A of X, having the value 1 for all elements of A and the value 0 for all elements of X not in A
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Dirichlet Function
In mathematics, a nowhere continuous function, also called an everywhere discontinuous function, is a function that is not continuous at any point of its domain. If f is a function from real numbers to real numbers, then f is nowhere continuous if for each point x there is an ε > 0 such that for each δ > 0 we can find a point y such that 0 < x − y < δ and f(x) − f(y) ≥ ε
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Nowhere Continuous
In mathematics, a nowhere continuous function, also called an everywhere discontinuous function, is a function that is not continuous at any point of its domain. If f is a function from real numbers to real numbers, then f is nowhere continuous if for each point x there is an ε > 0 such that for each δ > 0 we can find a point y such that 0 < x − y < δ and f(x) − f(y) ≥ ε
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Mathematical Singularity
In mathematics, a singularity is in general a point at which a given mathematical object is not defined, or a point of an exceptional set where it fails to be well-behaved in some particular way, such as differentiability. For example, the real function f ( x ) = 1 x displaystyle f(x)= frac 1 x has a singularity at x = 0, where it seems to "explode" to ±∞ and is not defined. The function g(x) = x (see absolute value) also has a singularity at x = 0, since it is not differentiable there. The algebraic curve defined by ( x , y ) : y 3 − x 2 = 0 displaystyle (x,y):y^ 3 -x^ 2 =0 in the (x, y) coordinate system has a singularity (called a cusp) at (0, 0). See Singular point of an algebraic variety for details on singularities in algebraic geometry
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International Standard Book Number
"ISBN" redirects here. For other uses, see ISBN (other).International Standard Book
Book
NumberA 13-digit ISBN, 978-3-16-148410-0, as represented by an EAN-13 bar codeAcronym ISBNIntroduced 1970; 48 years ago (1970)Managing organisation International ISBN AgencyNo. of digits 13 (formerly 10)Check digit Weighted sumExample 978-3-16-148410-0Website www.isbn-international.orgThe International Standard Book
Book
Number (ISBN) is a unique[a][b] numeric commercial book identifier. Publishers purchase ISBNs from an affiliate of the International ISBN Agency.[1] An ISBN is assigned to each edition and variation (except reprintings) of a book. For example, an e-book, a paperback and a hardcover edition of the same book would each have a different ISBN. The ISBN is 13 digits long if assigned on or after 1 January 2007, and 10 digits long if assigned before 2007
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PlanetMath
PlanetMath
PlanetMath
is a free, collaborative, online mathematics encyclopedia. The emphasis is on rigour, openness, pedagogy, real-time content, interlinked content, and also community of about 24,000 people with various maths interests. Intended to be comprehensive, the project is currently hosted by the University of Waterloo
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Continuous Function
In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output. Otherwise, a function is said to be a discontinuous function. A continuous function with a continuous inverse function is called a homeomorphism. Continuity of functions is one of the core concepts of topology, which is treated in full generality below. The introductory portion of this article focuses on the special case where the inputs and outputs of functions are real numbers. A stronger form of continuity is uniform continuity. In addition, this article discusses the definition for the more general case of functions between two metric spaces. In order theory, especially in domain theory, one considers a notion of continuity known as Scott continuity. Other forms of continuity do exist but they are not discussed in this article. As an example, consider the function h(t), which describes the height of a growing flower at time t
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Ed Pegg, Jr.
Ed Pegg Jr.
Ed Pegg Jr.
(born December 7, 1963) is an expert on mathematical puzzles and is a self-described recreational mathematician. He wrote an online puzzle column called Ed Pegg Jr.'s Math Games for the Mathematical Association of America
Mathematical Association of America
during the years 2003–2007. His puzzles have also been used by Will Shortz
Will Shortz
on the puzzle segment of NPR's Weekend Edition
Weekend Edition
Sunday. In 2000, he left NORAD
NORAD
to join Wolfram Research, where he collaborated on A New Kind of Science
A New Kind of Science
(NKS). In 2004 he started assisting Eric W. Weisstein at Wolfram MathWorld.[1] He has made contributions to several hundred MathWorld articles.[2] He was one of the chief consultants for Numb3rs. References[edit]^ MathWorld Headline News and About MathWorld
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The Wolfram Demonstrations Project
The Wolfram Demonstrations Project
Wolfram Demonstrations Project
is an organized, open-source[1] collection of small (or medium-size) interactive programs called Demonstrations, which are meant to visually and interactively represent ideas from a range of fields. It is hosted by Wolfram Research, whose stated goal is to bring computational exploration to the widest possible audience. At its launch, it contained 1300 demonstrations[2] but has grown to over 10,000
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Eric W. Weisstein
Eric Wolfgang Weisstein (born March 18, 1969) is an encyclopedist who created and maintains MathWorld and Eric Weisstein's World of Science (ScienceWorld). He is the author of the CRC Concise Encyclopedia of Mathematics. He currently works for Wolfram Research, Inc.Contents1 Education 2 Career2.1 Academic research 2.2 MathWorld, ScienceWorld
ScienceWorld
and Wolfram Research 2.3 Further scientific activities3 Footnotes 4 References 5 External linksEducation[edit] Weisstein holds a Ph.D. in planetary astronomy which he obtained from the California Institute of Technology's (Caltech) Division of Geological and Planetary Sciences in 1996 as well as an M.S. in planetary astronomy in 1993 also from Caltech. Weisstein graduated Cum Laude from Cornell University
Cornell University
with a B.A. in physics and a minor in astronomy in 1990
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MathWorld
MathWorld is an online mathematics reference work, created and largely written by Eric W. Weisstein. It is sponsored by and licensed to Wolfram Research, Inc.
Wolfram Research, Inc.
and was partially funded by the National Science Foundation's National Science Digital Library grant to the University of Illinois at Urbana–Champaign.Contents1 History 2 CRC lawsuit 3 See also 4 References 5 External linksHistory[edit] Eric W. Weisstein, the creator of the site, was a physics and astronomy student who got into the habit of writing notes on his mathematical readings. In 1995 he put his notes online and called it "Eric's Treasure Trove of Mathematics." It contained hundreds of pages/articles, covering a wide range of mathematical topics. The site became popular as an extensive single resource on mathematics on the web. Weisstein continuously improved the notes and accepted corrections and comments from online readers
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Michiel Hazewinkel
Michiel Hazewinkel
Michiel Hazewinkel
(born June 22, 1943) is a Dutch mathematician, and Emeritus Professor of Mathematics
Mathematics
at the Centre for Mathematics
Mathematics
and Computer and the University of Amsterdam, particularly known for his 1978 book Formal groups and applications and as editor of the Encyclopedia of Mathematics.Contents1 Biography 2 Publications 3 References 4 External linksBiography[edit] Born in Amsterdam
Amsterdam
to Jan Hazewinkel and Geertrude Hendrika Werner, Hazewinkel studied at the University of Amsterdam
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