In terms of current popular technologies: Any computer connected to the same Ethernet repeater or switch is a member of the same broadcast domain.

* Any simply connected solvable Lie group is isomorphic to a closed subgroup of the group of invertible upper triangular matrices of some rank, and any finite dimensional irreducible representation of such a group is 1 dimensional.

* Any simply connected nilpotent Lie group is isomorphic to a closed subgroup of the group of invertible upper triangular matrices with 1's on the diagonal of some rank, and any finite dimensional irreducible representation of such a group is 1 dimensional.

Any knot can be uniquely expressed as a connected sum of prime knots.

* Any two vertices in G can be connected by a unique simple path.

Any object so sacrificed or devoted to the Lord could not be redeemed (; ); and hence the idea of exterminating was connected with the word.

Any potentiometer may be connected as a rheostat.

Any number of transputers could be connected together over even longish links ( tens of metres ) to form a single computing " farm ".

It declares him to be a Suppressive Person and continues, " Any and all persons connected him are declared Potential Trouble Sources and are not to be Trained or Processed before they have presented evidence in writing (...) of handling or disconnecting.

Any timpani equipped with such a system may be considered machine timpani, although this term commonly refers to drums that use a single handle connected to a spider-type tuning mechanism.

To show that U ( n ) is connected, recall that any unitary matrix A can be diagonalized by another unitary matrix S. Any diagonal unitary matrix must have complex numbers of absolute value 1 on the main diagonal.

* Any clopen set is a union of ( possibly infinitely many ) connected components.

Any negative externalities in the hubs creates a ripple effect through the financial system and the economy ( and, the connected economies ) as a whole.

Any move that connected with the opponent would end the round, a loosely timed or borderline kick or punch would obtain half a yin-yang icon, while a well executed move would obtain a full icon.

Any other onboard interfaces ( such as serial and parallel ports ) had to be connected via flying leads to connectors which were mounted either on spaces provided by the case or brackets placed in unused expansion slot positions.

Any point that is rigidly connected to the body can be used as reference point ( origin of coordinate system L ) to describe the linear motion of the body ( the linear position, velocity and acceleration vectors depend on the choice ).

Any group scheme G of finite type is an extension of the connected component of the identity ( i. e., the maximal connected subgroup scheme ) by a constant group scheme.

Any “ nice ” space such as a manifold or CW complex is semi-locally simply connected.

Any connected Lie group can be built up by means of its infinitesimal generators ( a basis for the Lie algebra of the group ); with explicit if not always useful information given in the Baker – Campbell – Hausdorff formula.

A graph coloring is an assignment of one of k colors to a graph G so that the endpoints of each edge have different colors, for some number k. Any coloring corresponds to a homomorphism from G to a complete graph K < sub > k </ sub >: the vertices of K < sub > k </ sub > correspond to the colors of G, and f maps each vertex of G with color c to the vertex of K < sub > k </ sub > that corresponds to c. This is a valid homomorphism because the endpoints of each edge of G are mapped to distinct vertices of K < sub > k </ sub >, and every two distinct vertices of K < sub > k </ sub > are connected by an edge, so every edge in G is mapped to an adjacent pair of vertices in K < sub > k </ sub >.

Any inverter which is listed to the UL 1741 standard may be connected to a utility grid without the need for additional anti-islanding equipment, anywhere in the United States or other countries where UL standards are accepted.

Any non-commercial research or educational institution such as libraries, archives and schools may be connected for a yearly fee.

" Any act or omission by a body of workers, which is intended or which does result in any limitation, restriction, reduction, delatoriness in the performance of their duties connected to their employment "

* Any vector space V endowed with the identically zero Lie bracket becomes a Lie algebra.

Any one-dimensional Lie algebra over a field is abelian, by the antisymmetry of the Lie bracket.

* Any Lie group G defines an associated real Lie algebra.

* Any topologically closed subgroup of a Lie group is a Lie group.

Any Lie group G can be decomposed into discrete, simple, and abelian groups in a canonical way as follows.

# Any tangent vector at the identity of a Lie group can be extended to a left invariant vector field by left translating the tangent vector to other points of the manifold.

A weight on a Lie algebra g over a field F is a linear map λ: g → F with λ ( y )= 0 for all x, y in g. Any weight on a Lie algebra g vanishes on the derived algebra and hence descends to a weight on the abelian Lie algebra g /.

* Any Lie group gives a Lie groupoid with one object, and conversely.

* Any foliation gives a Lie groupoid.

Any smooth function on a symplectic manifold gives rise, by definition, to a Hamiltonian vector field and the set of all such form a subalgebra of the Lie Algebra of symplectic vector fields.

Any associative algebra A over the field K becomes a Lie algebra over K with the Lie bracket:

* Any Lie group with an infinite group of components G / G < sup > o </ sup > cannot be realized as an algebraic group ( see identity component ).

Any n-dimensional formal group law gives an n dimensional Lie algebra over the ring R, defined in terms of the quadratic part F < sub > 2 </ sub > of the formal group law.

Any finite-dimensional irreducible representation of a semisimple Lie group or Lie algebra can be constructed from the fundamental representations by a procedure due to Élie Cartan.

* Any member of the genus Eunectes, a group of large, aquatic snakes found in South America

Any normal subgroup has a corresponding quotient group, formed from the larger group by eliminating the distinction between elements of the subgroup.

Any formal or informal group — a family, a church, a club, a business, a trade union — may be said to have government.

" Any attempt to organize the group ... under a single authority would eliminate their independent initiatives, and thus reduce their joint effectiveness to that of the single person directing them from the centre.

Any symmetry group whose elements have a common fixed point, which is true for all finite symmetry groups and also for the symmetry groups of bounded figures, can be represented as a subgroup of orthogonal group O ( n ) by choosing the origin to be a fixed point.

However, in the case of a finitely presented group we know that not all the generators can be trivial ( Any individual generator could be, of course ).

* Any subgroup of a free group is free.

Any group of four students may run for office, but there must always be four students.

Any group that managed to find ways of reasoning effectively would reap benefits for all its members, increasing their fitness.

Any time during a triad conversation, group members can switch seats and one of the co-pilots can sit in the pilot ’ s seat.

Any group can be seen as a category with a single object in which every morphism is invertible ( for every morphism f there is a morphism g that is both left and right inverse to f under composition ) by viewing the group as acting on itself by left multiplication.