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.