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

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

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