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

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...

{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 , … ] )...

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...

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...

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

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:...

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:...

Venn's construction for six sets Venn's four-set diagram using ellipses Non-example: This Euler diagram is not a Venn diagram for four sets as it has only...

{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...