Triviality (mathematics)

In mathematics, the adjective trivial is frequently used for objects (for example, groups or topological spaces) that have a very simple structure. The noun triviality usually refers to a simple technical aspect of some proof or definition. The origin of the term in mathematical language comes from the medieval trivium curriculum. The antonym nontrivial is commonly used by engineers and mathematicians to indicate a statement or theorem that is not obvious or easy to prove.

Trivial and nontrivial solutions

In mathematics, the term trivial is frequently used for objects (for examples, groups or topological spaces) that have a very simple structure.

Examples include:

Trivial can also be used to describe solutions to an equation that have a very simple structure, but for the sake of completeness cannot be omitted. These solutions are called the trivial solutions. For example, consider the differential equation