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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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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).
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.
Jul 18, 2017 · Apply the concept of triviality to sets of solutions to problems in general, or category-theoretically, take something like Problem and go to empty, trivial, and degenerate problems (objects in the category) with, in turn, empty, trivial, and degenerate solutions.
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.
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.
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.
A comprehensive guide to the concept of Triviality in Mathematics. Learn about its meaning, examples, proofs, and the difference between trivial and non-trivial solutions.
