Trivial, according to Google dictionary is an adjective with the meaning "of little value or importance." Some synonyms include: unimportant, insignificant, inconsequential, etc. It appears the literal meaning does not apply in math, because Triviality or Trivially true means different things in different contexts making it more confusing. In simple language, what does the term mean?
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$\begingroup$My understanding is that the word trivial has essentially two different uses in math. One of its uses is for an argument or step in a proof that the author doesn't explicitly justify because they consider it clear or obvious, e.g. "It is trivial to show that...". I think it's important to be careful when using it like this, because what is obvious to one person may not be obvious to another. The second use is for an extremely simple and uninteresting example of a class of objects. There are many examples of this from the Wikipedia page you link, including the trivial one-element group, the empty set, or the trivial solution to a linear system (all variables are zero). An example of this usage might be "This result holds for all non-trivial groups."
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