- published: 03 Feb 2013
- views: 1193
A mathematical object is an abstract object arising in mathematics. The concept is studied in philosophy of mathematics.
In mathematical practice, an object is anything that has been (or could be) formally defined, and with which one may do deductive reasoning and mathematical proofs. Commonly encountered mathematical objects include numbers, permutations, partitions, matrices, sets, functions, and relations. Geometry as a branch of mathematics has such objects as hexagons, points, lines, triangles, circles, spheres, polyhedra, topological spaces and manifolds. Another branch—algebra—has groups, rings, fields, group-theoretic lattices, and order-theoretic lattices. Categories are simultaneously homes to mathematical objects and mathematical objects in their own right. In proof theory, proofs and theorems are also mathematical objects.
The ontological status of mathematical objects has been the subject of much investigation and debate by philosophers of mathematics.
In this first video of the series, we describe the nature of the problem of the existence of mathematical objects. We frame the discussion into the language of ontology and epistemology, that is, the theory of existence and the theory of knowledge. We look at Euclid's definition of a point and a line and see that these objects are not physical, so they must exist outside of time and space. That implies there must be an immaterial reality where these objects exist. Since we can know about these objects, then we must have an immaterial aspect of ourselves. We conclude by relating this to the Platonist doctrine of the immortality of the soul, as detailed in the Phaedo. Indications of topics to be explored in the rest of the series are discussed at the end.
George Hart describes in this video how to create physical models of mathematical objects, surveying some examples of surfaces and polytopes. http://www.simonsfoundation.org/multimedia/3-d-printing-of-mathematical-models/
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Mathematical object A mathematical object is an abstract object arising in mathematics.The concept is studied in philosophy of mathematics. -Video is targeted to blind users Attribution: Article text available under CC-BY-SA image source in video https://www.youtube.com/watch?v=n9gskjq0ok0
Explanation of a mathematical object
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Japanese mathematics professor Kokichi Sugihara spends much of his time in a world where up is down and three dimensions are really only two. Professor Sugihara is one of the world's leading exponents of optical illusion, a mathematical art-form that he says could have application in the real world. For more news and videos visit ☛ http://ntd.tv Follow us on Twitter ☛ http://twitter.com/NTDTelevision Add us on Facebook ☛ http://on.fb.me/s5KV2C Three sloped ramps are aligned along three of the four sides of a square. Each ramp appears to be sloped in the same direction but when a marble is placed at one end of the ramp it seems to defy gravity. It's called an "anti-gravity slide". Only when the the entire structure is turned 180 degrees, is the illusion revealed. Japanese mathematics pr...
Mappings that don't preserve structure are meaningless ?
A novel mathematical object !
A nice little mechanical calculator I bought for about a tenner. Aperiodical post: http://aperiodical.com/2016/04/maths-object-correntator/
Built-in Objects Functions
A mathematical object is an abstract object arising in mathematics. - Video generated using Wikipedia data - Background music by www.bensound.com