Nontrivial - Examples

Examples

• In mathematics, it is often important to find factors of an integer number N. Any number N has four obvious factors: ±1 and ±N. These are called "trivial factors". Any other factor, if any exist, would be called "nontrivial".

• The matrix equation AX=0, where A is a fixed matrix, X is an unknown vector, and 0 is the zero vector, has an obvious solution X=0. This is called the "trivial solution". If it has other solutions X≠0, they would be called "nontrivial"

• In the mathematics of group theory, there is a very simple group with just one element in it; this is often called the "trivial group". All other groups, which are more complicated, are called "nontrivial".

• In the graph theory the trivial graph is a graph which have only 1 vertex and no edges.

• Database theory has a concept called functional dependency, written . It is obvious that the dependence is true if Y is a subset of X, so this type of dependence is called "trivial". All other dependences, which are less obvious, are called "nontrivial".

• The differential equation with boundary conditions is important in math and physics, for example describing a particle in a box in quantum mechanics, or standing waves on a string. It always has the solution . This solution is considered obvious and is called the "trivial" solution. In some cases, there may be other solutions (sinusoids), which are called "nontrivial".