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People also ask
What does 'trivial' mean in mathematics?
Where does the word 'trivial' come from?
What is a trivial solution?
What is the difference between trivial and non-trivial solutions?
What is an example of a trivial equation?
What is the second meaning of trivial?
In mathematics, the adjective trivial is often used to refer to a claim or a case which can be readily obtained from context, or an object which possesses a simple structure (e.g., groups, topological spaces).
Triviality Meaning in Maths. In Mathematics, triviality is a property of objects having simple structures. The word trivial is used for simple and evident concepts or things, such as – topological spaces and groups that have a simple arrangement. The antonym of trivial is non-trivial.
There are two meanings of the word "trivial" in mathematics. The first, as you rightly pointed out, is strictly defined and appears in most mathematical fields. By strictly defined, I mean that if you say "the trivial solution to the ODE $y'=g(x) y$ ", I know with certainty that you mean the solution $y\equiv 0$ .
Trivial. A solution or example that is ridiculously simple and of little interest. Often, solutions or examples involving the number 0 are considered trivial. Nonzero solutions or examples are considered nontrivial. For example, the equation x + 5 y = 0 has the trivial solution x = 0, y = 0.
Nov 8, 2016 · A solution which does not consist of all zeros is not trivial. The trivial solution means that all the variables are zero (i.e. the solution is the zero vector). If the system is homogeneous and it has a unique solution, it will always be the zero solution.
5 days ago · More generally, the word "trivial" is used to describe any result which requires little or no effort to derive or prove. The word originates from the Latin trivium, which was the lower division of the seven liberal arts in medieval universities (cf. quadrivium).
In mathematics, the adjective trivial is often used to refer to a claim or a case which can be readily obtained from context, or an object which possesses a simple structure (e.g., groups, topological spaces).
