Object (mathematics) | Wikipedia audio article

Описание: This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Mathema...


00:00:24 1 Cantorian framework
00:00:49 2 Foundational paradoxes
00:01:14 3 Category theory
00:01:39 4 See also



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SUMMARY
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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, integers, integer partition, or expressions. Combinatorics (a branch of mathematics) has such objects as:

permutations, derangements, combinations.Set theory (a branch of mathematics) has such objects as:

sets, set partitions,
functions, and relations.Geometry (a branch of mathematics) has such objects as:

points, lines, line segments,
polygons (triangles, squares, pentagons, hexagons, ...), circles, ellipses, parabolas, hyperbolas,
polyhedra (tetrahedrons, cubes, octahedrons, dodecahedrons, icosahedrons, ), spheres, ellipsoids, paraboloids, hyperboloids, cylinders, cones.Graph theory (a branch of mathematics) has such objects as:

graphs, trees, nodes, edgesTopology (a branch of mathematics) has such objects as:

topological spaces and manifolds.Linear algebra (a branch of mathematics) has such objects as:

scalars, vectors, matrices, tensors.Abstract algebra (a branch of mathematics) has such objects as:

groups,
rings, modules,
fields, vector spaces,
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.