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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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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.
Learn triviality meaning in terms of Mathematics. Also, learn the proof of trivial with examples and other terminology used such as trivial solutions, trivial factors, trivial group, trivial graph.
2) Trivial solutions to a problem, i.e. y =y′ y = y ′ has a trivial solutions as a differential equation, y = 0 y = 0. 3) Trivial factors of a number or polynomial, i.e. 1, n|n 1, n | n ∀n ∈ N ∀ n ∈ N. What these two meanings have in common is that they are defined in this way.
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.
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
And there can be an argument about how quickly and easily a problem should be recognized for the problem to be treated as trivial. The following examples show the subjectivity and ambiguity of the triviality judgement.
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.
