Portal:Mathematics
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Mathematics is the study of representing and reasoning about abstract objects (such as numbers, points, spaces, sets, structures, and games). Mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences. Applied mathematics, the branch of mathematics concerned with application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries and sometimes leads to the development of entirely new mathematical disciplines, such as statistics and game theory. Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, and practical applications for what began as pure mathematics are often discovered. (Full article...)
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- ... that mathematician Mathias Metternich was one of the founders of the Jacobin club of the Republic of Mainz?
- ... that Ukrainian baritone Danylo Matviienko, who holds a master's degree in mathematics, appeared as Demetrius in Britten's opera A Midsummer Night's Dream at the Oper Frankfurt?
- ... that The Math Myth advocates for American high schools to stop requiring advanced algebra?
- ... that the 1914 Lubin vault fire in Philadelphia destroyed several thousand unique early silent films?
- ... that the mathematical infinity symbol ∞ may be derived from the Roman numerals for 1000 or for 100 million?
- ... that the word algebra is derived from an Arabic term for the surgical treatment of bonesetting?
- ... that Coastal Carolina football coach Chad Staggs has degrees in math education and tourism management?
- ... that the discovery of Descartes' theorem in geometry came from a too-difficult mathematics problem posed to a princess?
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- ...that the set of rational numbers is equal in size to the set of integers; that is, they can be put in one-to-one correspondence?
- ...that there are precisely six convex regular polytopes in four dimensions? These are analogs of the five Platonic solids known to the ancient Greeks.
- ...that it is unknown whether π and e are algebraically independent?
- ...that a nonconvex polygon with three convex vertices is called a pseudotriangle?
- ...that it is possible for a three-dimensional figure to have a finite volume but infinite surface area, such as Gabriel's Horn?
- ... that as the dimension of a hypersphere tends to infinity, its "volume" (content) tends to 0?
- ...that the primality of a number can be determined using only a single division using Wilson's Theorem?
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The real number denoted by the recurring decimal 0.999… is exactly equal to 1. In other words, "0.999…" represents the same number as the symbol "1". Various proofs of this identity have been formulated with varying rigour, preferred development of the real numbers, background assumptions, historical context, and target audience.
The equality has long been taught in textbooks, and in the last few decades, researchers of mathematics education have studied the reception of this equation among students, who often reject the equality. The students' reasoning is typically based on one of a few common erroneous intuitions about the real numbers; for example, a belief that each unique decimal expansion must correspond to a unique number, an expectation that infinitesimal quantities should exist, that arithmetic may be broken, an inability to understand limits or simply the belief that 0.999… should have a last 9. These ideas are false with respect to the real numbers, which can be proven by explicitly constructing the reals from the rational numbers, and such constructions can also prove that 0.999… = 1 directly. (Full article...)
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