The joking sense of
trivial noted above is more what I would call
obvious, a
subjective judgement, whereas
trivial is a legitimate
mathematical term that is similar to
degenerate The trivial case is the one that falls out immediately from the
definition without having to do
any work.
Under degenerate the example is given of a circle of radius 0: what you get is a point, it isn't really a circle at all, but it might be convenient to classify it as one if you want your set of possible radii to include 0. We can bring all three of these terms together with factorial:
0! = 1 is the degenerate case. We define this identity for consistency, but we're not really applying the factorial operation, not even '"zero times".
1! = 1 is the trivial case. We set up the conditions for applying the recursive operation, but it turns out that there's nothing left to do. The initial case in mathematical induction is usually trivial.
2! = 2 x 1 is non-trivial. At least some actual working is involved.
2! is however obvious. In fact so is 1000000!, because it's obvious how to do it, even if you don't offhand know or haven't got the time to do it just now, or even if the procedure would take impossibly long but still doesn't present any difficulty in principle.
I wonder how much the
derogatory meaning of the word derives from each of the two older meanings. A three-way
crossing is a place where the common people resort, or where you see all sorts of people going past, so it comes to mean
commonplace or not worth seeking out. But the other meaning is the more
disputatious branch of the
liberal arts, the
trivium. The three trivial arts of
rhetoric,
logic, and
grammar would have been seen much as what we now call the
humanities or
soft sciences, with no final answers, whereas the
quadrivial arts of arithmetic, geometry, astronomy, and music had the cachet of objectivity. Perhaps the trivia acquired a reputation for
sophistry,
frivolity, and
foolishness.