If this happens, there may be some class conflict in the South, with school boards and school teachers taking the middle-class position.

If this threefold division of costs were to have its counterpart in the actual rates of charge for service, as it actually does have in some rates, there would result a three-part rate for any one class of service.

If the automorphisms of an object X form a set ( instead of a proper class ), then they form a group under composition of morphisms.

If at least one class of creditors votes against the plan and thus objects, the plan may nonetheless be confirmed if the requirements of cramdown are met.

If that class is not available, or unknown at compile time, the application simply won't compile.

If ~ is an equivalence relation on X, and P ( x ) is a property of elements of X, such that whenever x ~ y, P ( x ) is true if P ( y ) is true, then the property P is said to be well-defined or a class invariant under the relation ~.

* If is the set of all cars, and is the equivalence relation " has the same color as ", then one particular equivalence class consists of all green cars.

The " diamond problem " ( sometimes referred to as the " deadly diamond of death ") is an ambiguity that arises when two classes B and C inherit from A, and class D inherits from both B and C. If D calls a method defined in A ( and does not override the method ), and B and C have overridden that method differently, then from which class does it inherit: B, or C?

If a business can only be advantageously carried on by a large capital, this in most countries limits so narrowly the class of persons who can enter into the employment, that they are enabled to keep their rate of profit above the general level.

If one follows broader linguistic tradition and counts singular and plural as belonging to the same class, then Swahili has 8 or 9 noun classes, Sotho has 11 and Ganda has 10.

If the distribution of income within a country is skewed, a small wealthy class can increase per capita income far above that of the majority of the population.

If there was a separate class of warriors, it probably consisted of single young men.

If new members are added to a serializable class, they can be tagged with the attribute to allow previous versions of the object to be deserialized without error.

If a class requires custom serialization ( for example, it requires certain cleanup actions done on dumping / restoring ), it can be done by implementing 2 methods: and.

⟨ H ⟩, be the group generated by H. Then the word problem in H < sup >*</ sup > is solvable: given two words h, k in the generators H of H < sup >*</ sup >, write them as words in X and compare them using the solution to the word problem in G. It is easy to think that this demonstrates a uniform solution the word problem for the class K ( say ) of finitely generated groups that can be embedded in G. If this were the case the non-existence of a universal solvable word problem group would follow easily from Boone-Rogers.

Only much later in the story is the secret revealed, when Malik is hypnotized by Hagbard Celine to recall suppressed memories of his first-grade teacher conditioning his class to ignore the fnords: " If you don't see the fnord it can't eat you, don't see the fnord, don't see the fnord ..."

If this object is a class of transformations ( such as " isomorphism " or " permutation "), it implies the equivalence of objects one of which is the image of the other under such a transformation.

) If formulated in von Neumann – Bernays – Gödel set theory, the surreal numbers are the largest possible ordered field ; all other ordered fields, such as the rationals, the reals, the rational functions, the Levi-Civita field, the superreal numbers, and the hyperreal numbers, are subfields of the surreals ; it has also been shown that the maximal class hyperreal field is isomorphic to the maximal class surreal field.

A vacuous truth is a truth that is devoid of content because it asserts something about all members of a class that is empty or because it says " If A then B " when in fact A is inherently false.

If treated as a class, as in the Cronquist system, they may be called the Magnoliopsida after the type genus Magnolia.

) If we use a nondeterministic machine instead, we get the class NEXPSPACE, which is equal to EXPSPACE by Savitch's theorem.

If any program needed to create an instance of that class, it got whatever was the current centrally registered implementation.

If Af are the projections associated with the primary decomposition of T, then each Af is a polynomial in T, and accordingly if a linear operator U commutes with T then U commutes with each of the Af, i.e., each subspace Af is invariant under U.

If is an equivalence relation on, and is a property of elements of such that whenever, is true if is true, then the property is said to be an invariant of, or well-defined under the relation.

If a spatial extra dimension is of radius R, the invariant mass of such standing waves would be M < sub > n </ sub > = nh / Rc with n an integer, h being Planck's constant and c the speed of light.

* If an R module is finitely generated and projective ( that is, a progenerator ), then the endomorphism ring of the module and R share all Morita invariant properties.

If one bends and deforms the surface, its Euler characteristic, being a topological invariant, will not change, while the curvatures at some points will.

* If two polyhedra are scissors-congruent, then they have the same Dehn invariant.

If time is the basis for house division, a difference must be made for whether the houses are based on invariant equal hours ( each house represents 2 hours of the sun's apparent movement each day ) or temporal hours ( daytime and night-time divided into six equal parts, but here the temporal hours will vary according to season and latitude.

If objects within a system are in relative motion, then the invariant mass of the whole system will differ from the sum of the objects ' rest masses.

If there is one dominant particle which was not detected during an experiment, a plot of the invariant mass will show a sharp peak at the mass of the missing particle.

If a test is invariant to some group difference ( e. g. gender ) in one population ( e. g. England ) it does not automatically mean that it is also invariant in another population ( e. g. Japan ).

* If the Lagrangian is invariant under a symmetry, then the resulting equations of motion are also invariant under that symmetry.

If instead of looking at the full scheme structure on the n-torsion, one considers only the geometric points, one obtains a new invariant for varieties in characteristic p ( the so-called p-rank when n = p ).

If, for example, we simply look at a curve in the real affine plane there might be singular P modulo the stalk, or alternatively as the sum of m ( m − 1 )/ 2, where m is the multiplicity, over all infinitely near singular points Q lying over the singular point P. Intuitively, a singular point with delta invariant δ concentrates δ ordinary double points at P. For an irreducible and reduced curve and a point P we can define δ algebraically as the length of where is the local ring at P and is its integral closure.

* If G is compact, it has a Riemannian metric invariant under left and right translations, and the exponential map is the exponential map of this Riemannian metric.

If there is a field ( often a background field ) which acquires an expectation value ( not necessarily a vacuum expectation value ) which is not invariant under the symmetry in question, we say that the system is in the ordered phase, and the symmetry is spontaneously broken.

If the operator is translation invariant, that is when L has constant coefficients with respect to x, then the Green's function can be taken to be a convolution operator, that is,

If has invariant basis number, then by definition any two bases have the same cardinality.

If the highest weight is dominant and integral ( a weight μ is dominant and integral if μ satisfies the condition that is a non-negative integer for all i ), then the weight spectrum of the irreducible representation is invariant under the Weyl group for G, and the representation is integrable.

If we choose variables that are invariant to homology, then we can reduce the order of the Lane – Emden equation by one.

If, as in this case, we can find a unique such invariant measure, that solves the problem of formulating accurately what ' random line ' means ; and expectations become integrals with respect to that measure.