Difference between revisions of "Mathematical object"
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* Matrices | * Matrices | ||
* [[Set (mathematics)|Sets]] | * [[Set (mathematics)|Sets]] | ||
| − | * Functions | + | * [[Function (mathematics)|Functions]] |
* Relations | * Relations | ||
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The ontological status of mathematical objects has been the subject of much investigation and debate by philosophers of mathematics. | The ontological status of mathematical objects has been the subject of much investigation and debate by philosophers of mathematics. | ||
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| + | == Objects not given with their structure == | ||
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| + | Mathematical objects are not given to us with their structure. | ||
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| + | Rather, each mathematical theory describes its objects by some of their properties, precisely those that are put as axioms at the foundations of the theory. | ||
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| + | == Mathematical functions == | ||
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| + | [[Function (mathematics)|Functions]] are important mathematical objects. Usually they form infinite-dimensional spaces, as noted already by Riemann and elaborated in the 20th century by [[functional analysis]]. | ||
== See also == | == See also == | ||
Revision as of 21:15, 3 September 2016
A mathematical object is an abstract object arising in philosophy of mathematics and mathematics itself.
Commonly encountered mathematical objects include:
- Numbers
- Permutations
- Partitions
- Matrices
- Sets
- Functions
- Relations
Geometry as a branch of mathematics has such objects as:
- Points
- Lines
- Circles
- Triangles
- Squares
- Hexagons
- Spheres
- Polyhedra
- Topological spaces
- Manifolds
Algebra as a branch includes objects such as:
- Groups
- Rings
- Fields
- Group-theoretic lattices
- Order-theoretic lattices
Categories are simultaneously homes to mathematical objects and mathematical objects in their own right.
The ontological status of mathematical objects has been the subject of much investigation and debate by philosophers of mathematics.
Contents
Objects not given with their structure
Mathematical objects are not given to us with their structure.
Rather, each mathematical theory describes its objects by some of their properties, precisely those that are put as axioms at the foundations of the theory.
Mathematical functions
Functions are important mathematical objects. Usually they form infinite-dimensional spaces, as noted already by Riemann and elaborated in the 20th century by functional analysis.
See also
- Abstraction (mathematics)
- Abstract object
- Expression (mathematics)
- Foundations of mathematics
- Mathematical notation
- Mathematical structure
- Mathematics
- Object (computer science)
- Operation (mathematics)
- Permutation
- Philosophy of mathematics
- Value (mathematics)
External links
- Mathematical object @ Wikipedia
