trit = T = troff

trivial adj.

1. Too simple to bother detailing. 2. Not worth the speaker's time. 3. Complex, but solvable by methods so well known that anyone not utterly cretinous would have thought of them already. 4. Any problem one has already solved (some claim that hackish `trivial' usually evaluates to `I've seen it before'). Hackers' notions of triviality may be quite at variance with those of non-hackers. See nontrivial, uninteresting.

The physicist Richard Feynman, who had the hacker nature to an amazing degree (see his essay "Los Alamos From Below" in "Surely You're Joking, Mr. Feynman!"), defined `trivial theorem' as "one that has already been proved".

--Jargon File, autonoded by rescdsk.

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In mathematics, a term used by professors (and students soon thereafter) to signify insignificance:

"At least one zero of f(x)=x^3-x is trivial."

In matrices, there is a trivial vector space x to the equation Ax=0 for any given matrix A. Sometimes this space amounts to x=0.

Some examples of "nontrivial" items:

The solution set of vectors x in the equation Ax=0 for x != 0.

The number of primes less than or equal to some given number N.

The complete factorization of any particular large number (e.g. (10^174)-7).
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.

Triv"i*al (?), a. [L. trivialis, properly, that is in, or belongs to, the crossroads or public streets; hence, that may be found everywhere, common, fr. trivium a place where three roads meet, a crossroad, the public street; tri- (see Tri-) + via a way: cf. F. trivial. See Voyage.]

1.

Found anywhere; common.

[Obs.]

2.

Ordinary; commonplace; trifling; vulgar.

As a scholar, meantime, he was trivial, and incapable of labor. De Quincey.

3.

Of little worth or importance; inconsiderable; trifling; petty; paltry; as, a trivial subject or affair.

The trivial round, the common task. Keble.

4.

Of or pertaining to the trivium.

Trivial name Nat. Hist., the specific name. (b) Chem. The common name, not describing the structure and from which the structure cannot be deduced; -- contrasted with systematic name.

© Webster 1913.


Triv"i*al, n.

One of the three liberal arts forming the trivium.

[Obs.]

Skelton. Wood.

 

© Webster 1913.

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