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Trivial


Related to or being the mathematically most simple case. More generally, the word "trivial" is used to describe any result which requires little or no effort to derive or prove. The word originates from the Latin trivium, which was the lower division of the seven liberal arts in medieval universities (cf. quadrivium).

According to the Nobel Prize-winning physicist Richard Feynman (Feynman 1997), mathematicians designate any theorem as "trivial" once a proof has been obtained--no matter how difficult the theorem was to prove in the first place. There are therefore exactly two types of true mathematical propositions: trivial ones, and those which have not yet been proven.

The opposite of a trivial theorem is a "deep theorem."


See also

Deep Theorem, Degenerate, Frivolous Theorem of Arithmetic, Monster-Barring, Pathological, Proof, Theorem, Trivial Basis, Trivial Bundle, Trivial Group, Trivial Loop, Trivial Module, Trivial Representation, Trivial Ring, Trivial Topology, Trivialization, Trivium

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References

Feynman, R. P. "A Different Set of Tools." In 'Surely You're Joking, Mr. Feynman!': Adventures of a Curious Character. New York: W. W. Norton, pp. 69-72, 1997.

Referenced on Wolfram|Alpha

Trivial

Cite this as:

Weisstein, Eric W. "Trivial." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Trivial.html

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