# Mathematical object

[https://en.wikipedia.org/wiki/Mathematical\_object](https://en.wikipedia.org/wiki/Mathematical_object)

A mathematical object is an abstract object arising in mathematics. The concept is studied in philosophy of mathematics.

Key topics

[https://en.wikipedia.org/wiki/Category:Mathematical\_objects](https://en.wikipedia.org/wiki/Category:Mathematical_objects)

**Mathematical object** is anything that can be formally defined and used in deductive reasoning and mathematical proofs. In modern math, most mathematical objects are defined in terms of sets.

Mathematical objects:

* permutations
* combinations
* partitions
* relations
* functions
* proofs
* theorems

**Discrete Structures** aid us in modelling the world in a way that enables us to think about it rigorously and computationally.

**Mathematical statements** have their own moderately complex taxonomy, being divided into:

* axioms
* conjectures
* theorems
* lemmas
* corollaries

An **axiom** or **postulate** is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments.

A **conjecture** is a conclusion or proposition based on incomplete information, for which no proof or disproof has yet been found. Conjectures such as the `Riemann hypothesis` (still a conjecture) or `Fermat's Last Theorem` (which was a conjecture until proven in 1995 by Andrew Wiles) have shaped much of mathematical history as new areas of mathematics are developed in order to prove them.

A **theorem** is a statement that has been proven on the basis of previously established statements, such as other theorems, and generally accepted statements, such as axioms. A theorem is a logical consequence of the axioms. The proof of a mathematical theorem is a logical argument for the theorem statement given in accord with the rules of a deductive system. The proof of a theorem is often interpreted as justification of the truth of the theorem statement.

A **lemma** is a proven proposition which is used as a stepping stone to a larger result rather than as a statement of interest by itself.

A **corollary** is a statement that readily follows from a previous statement or proof.

[https://en.wikipedia.org/wiki/Mathematical\_object](https://en.wikipedia.org/wiki/Mathematical_object)

MATHEMATICAL OBJECTS: Introduction [https://web.archive.org/web/20081014205857/http://www.abstractmath.org/MM//MMMathObj.htm](https://web.archive.org/web/20081014205857/http://www.abstractmath.org/MM/MMMathObj.htm)
