Nontrivial

Nontrivial is the opposite of trivial. In contexts where trivial has a formal meaning, nontrivial is its antonym.

It is a term common among communities of engineers and mathematicians, to indicate a statement or theorem that is not obvious or easy to prove.

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Other articles related to "nontrivial":

Pontryagin Class - Properties
... For example, up to vector bundle isomorphism, there is a unique nontrivial rank 10 vector bundle over the 9-sphere ... Moreover, this vector bundle is stably nontrivial, i.e ... the Whitney sum of with any trivial bundle remains nontrivial ...
Bass–Serre Theory - Trivial and Nontrivial Actions
... Typically, only nontrivial actions on trees are studied in Bass–Serre theory since trivial graphs of groups do not carry any interesting algebraic information ... that a finitely generated group has more than one end if and only if this group admits a nontrivial splitting over finite subroups that is, if and only if the group admits a ... with Kazhdan's property (T) then G does not admit any nontrivial splitting, that is, that any action of G on a tree X without edge-inversions has a global fixed vertex ...
Jacobi Sum
... For example, when the character is nontrivial, J(, ) = /, analogous to the formula for the beta function in terms of gamma functions ... Since the nontrivial Gauss sums have absolute value p1/2, it follows that J(, ) also has absolute value p1/2 when the characters, are nontrivial ... Jacobi sums J lie in smaller cyclotomic fields than do the nontrivial Gauss sums ...
Nontrivial - Examples
... Any other factor, if any exist, would be called "nontrivial" ... If it has other solutions X≠0, they would be called "nontrivial" In the mathematics of group theory, there is a very simple group with just one element in it this is often called the "trivial group" ... which are more complicated, are called "nontrivial" ...
Satellite Knot
... described as follows start by taking a nontrivial knot lying inside an unknotted solid torus ... Here "nontrivial" means that the knot is not allowed to sit inside of a 3-ball in and is not allowed to be isotopic to the central core curve of the ... Then tie up the solid torus into a nontrivial knot ...