Mathematical Group (Noun)
Meaning
A set that is closed, associative, has an identity element and every element has an inverse.
Classification
Nouns denoting cognitive processes and contents.
Examples
- The concept of a mathematical group is fundamental in abstract algebra, as it forms the basis for many other algebraic structures.
- The integers under addition form a mathematical group, as the sum of any two integers is an integer, and each integer has an additive inverse.
- A mathematical group is often represented using the Cayley table, a square table that describes the binary operation of the group.
- In calculus, the set of invertible matrices under matrix multiplication is a mathematical group, which is essential for solving systems of linear differential equations.
- The set of rotations in three-dimensional space forms a mathematical group, as the composition of any two rotations is a rotation, and each rotation has an inverse rotation.