Often, solutions or examples involving the number zero are considered trivial. Nonzero solutions or examples are considered nontrivial. For example, the equation x + 5y = 0 has the trivial solution (0, 0). Nontrivial solutions include (5, –1) and (–2, 0.4).

What is the difference between trivial and nontrivial?

The noun triviality usually refers to a simple technical aspect of some proof or definition. ... The opposite of trivial is nontrivial, which is commonly used to indicate that an example or a solution is not simple, or that a statement or a theorem is not easy to prove.

What does it mean when a system has a nontrivial solution?

If the system has a solution in which not all of the x1,⋯,xn are equal to zero, then we call this solution nontrivial . The trivial solution does not tell us much about the system, as it says that 0=0! ... Not only will the system have a nontrivial solution, but it also will have infinitely many solutions.