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
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
, 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
, and foolishness