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- Triviality is used to describe a result that needs very less or no effort to prove or derive it. Its synonyms are unimportance, insignificance, in-consequence, etc. Richard Feynman, Nobel Prize winner, stated- “a trivial theorem is a theorem whose proof has been obtained once”.
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Examples of triviality. Example 1. Trivial Solution. Consider the formula x + 3 equals x + 3. This equation has a simple solution: x = any real value. This is because subtracting x from both sides of the equation results in 3 = 3, which is always true regardless of x’s value.
The following examples show the subjectivity and ambiguity of the triviality judgement. Triviality also depends on context. A proof in functional analysis would probably, given a number, trivially assume the existence of a larger number.
The definition of the word "trivial" is a matter of consensus, and that consensus can change even among mathematicians. It is important to not that you may claim something is trivial only if a vast majority of mathematicians in your field also consider it trivial.
Triviality refers to the process of obtaining results from a context or an object with little or no effort. The objects used in these situations have simple topological structures. Graph theory, group theory and matrix are some common examples of triviality.
- Arpita Srivastava
In Mathematics, we define triviality as a property of objects that have simple structures. The word trivial is basically used for very simple and evident concepts or things, for example – topological spaces and groups have a very simple arrangement.
TRIVIALITY definition: 1. something that is not important: 2. the state of not being important: 3. something that is not…. Learn more.
