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In mathematics, a Cauchy sequence is a sequence whose elements become arbitrarily close to each other as the sequence progresses. More precisely, given...

In mathematics, and more specifically in abstract algebra, a *-algebra (or involutive algebra; read as "star-algebra") is a mathematical structure consisting...

In mathematics, the concept of a measure is a generalization and formalization of geometrical measures (length, area, volume) and other common notions...

In algebraic number theory, an algebraic integer is a complex number that is integral over the integers. That is, an algebraic integer is a complex root...

In mathematics, more specifically in the field of group theory, a solvable group or soluble group is a group that can be constructed from abelian groups...

In mathematics, a linear form (also known as a linear functional, a one-form, or a covector) is a linear map from a vector space to its field of scalars...

In mathematics, a Lie group (pronounced /liː/ LEE) is a group that is also a differentiable manifold, such that group multiplication and taking inverses...

stabilizers are finite, hence the stack is Deligne–Mumford. One simple non-example of a Deligne–Mumford stack is [ p t / C ∗ ] {\displaystyle [pt/\mathbb...

5-minute search and accidentally scare him from going outside. In this non-example, learning to open doors that lead outside resulted in consequences that...

In category theory, a branch of mathematics, a Krull–Schmidt category is a generalization of categories in which the Krull–Schmidt theorem holds. They...

In mathematics, a Lie algebra g {\displaystyle {\mathfrak {g}}} is solvable if its derived series terminates in the zero subalgebra. The derived Lie algebra...

of subgroups A and B is a subgroup if and only if A ⊆ B or B ⊆ A. A non-example: 2 Z ∪ 3 Z {\displaystyle 2\mathbb {Z} \cup 3\mathbb {Z} } is not a subgroup...

{Z} [z]}{(z^{5}-1)}}\right)} is a morphism of finite type. A simple non-example of a morphism of finite-type is Spec ⁡ ( k [ x 1 , x 2 , x 3 , … ] )...

A relation is connex if and only if its complement is asymmetric. A non-example is the "less than or equal" relation ≤ {\displaystyle \leq } . This is...

In mathematics, Kan complexes and Kan fibrations are part of the theory of simplicial sets. Kan fibrations are the fibrations of the standard model category...

In algebraic geometry and commutative algebra, a ring homomorphism f : A → B {\displaystyle f:A\to B} is called formally smooth (from French: Formellement...

graph? These are all necessarily members of the class #P as well. As a non-example, consider the case of counting solutions to a 1-satisfiability problem:...

and smooth! Non-examples of pure mate have been composed. In the given non-example, the black king cannot move to either c5 or e5 for the same two reasons:...

In mathematics, specifically in representation theory, a semisimple representation (also called a completely reducible representation) is a linear representation...

{2}{x_{n}}}{\bigr )}} is Cauchy, but has no rational limit (cf. Cauchy sequence § Non-example: rational numbers). More generally, any sequence of rational numbers...