Trivial

Something that is trivial (and triviality etc.) is something that anyone can grasp, understand, and explain to others, as opposed to something sublime, transcendental etc.

The word trivial comes from Latin, and is originally a word for the kind of things discussed in a trivium, a crossroads where three roads meet.

In the Roman empire a trivium would often have a tavern (Latin: taverna) or similar, where trivial things could be discussed, as opposed to the things discussed in other locations.

Mathematical use of the word trivial

In mathematics the term is frequently used for special cases that have a very simple structure, but for completeness sake can not be ignored. For non-mathematicians, they are often more difficult to understand than other simple cases. Examples include:

• empty set
• trivial group

Another example, when we consider the differential equation

Df=f

where f represents any function, and D the differential operator, we have the trivial solution

f = 0

and the nontrivial solution

f = e^x

See Also

• Trivial Pursuit, Trivia.