Similarly, although a subset of the real numbers that is not Lebesgue measurable can be proven to exist using the axiom of choice, it is consistent that no such set is definable.

Similarly, the subset order ⊆ on the subsets of any given set is antisymmetric: given two sets A and B, if every element in A also is in B and every element in B is also in A, then A and B must contain all the same elements and therefore be equal:

Similarly, a consequentialist theory may aim at the maximization of a particular virtue or set of virtues.

Similarly, the set of rational numbers in the closed interval is not compact: the sets of rational numbers in the intervals and cover all the rationals in for but this cover does not have a finite subcover.

Similarly, the set of organisms that can potentially be present in an area can also have a major impact on ecosystems.

Similarly for p ( 2 ), the set of limit points of p ( 1 ), and so on.

Similarly, in an edict of the Emperor Diocletian from AD 303, which set maximum prices of goods and services, the price of saddles, halters, and bridles are enumerated, as well as the price of a veterinarian for " cutting the hair and hoof of each animal.

Similarly, the most popular Arthurian tale throughout this period seems to have been that of Tom Thumb, which was told first through chapbooks and later through the political plays of Henry Fielding ; although the action is clearly set in Arthurian Britain, the treatment is humorous and Arthur appears as a primarily comedic version of his romance character.

Similarly, the set of all solutions to Einstein's field equations is simpler than a specific solution.

Similarly, in the power formulation, power can be distributed by generating a set of rays from the radiating element in the same way, and spreading the power to be distributed equally between each element a ray hits.

Similarly the set of all vectors in which is rational for all i is a countable dense subset of ; so for every the-dimensional Euclidean space is separable.

Similarly, Watson's appeal was successful, and the verdict was set aside pending a new trial.

Similarly, the additive group Z of integers is not simple ; the set of even integers is a non-trivial proper normal subgroup.

Similarly, the question of whether there exists a set whose cardinality is between | S | and | P ( S )| for some infinite S leads to the generalized continuum hypothesis.

Similarly, his conducting technique as described by contemporary sources appears to set the groundwork for the clarity and precision favoured in the French School of conducting right up to the present, exemplified by such figures as Pierre Monteux, Désiré-Émile Inghelbrecht, Paul Paray, Charles Munch, André Cluytens, Pierre Boulez and Charles Dutoit.

Similarly, once it is determined which substrates are ubiquitinated by each ligase, determining the set of ligases expressed in a particular cell type will be helpful.

Similarly, Henry Purcell wrote the opera " Dido and Aeneas ", which is based on themes from Classical Antiquity and is set in the immediate aftermath of the Trojan War ; yet, he provided Dido ( Queen of Carthage ) with a sister called " Belinda "-a name which is probably of Germanic origin and certainly did not exist before the Middle Ages.

Similarly, the saying, if it walks like a duck and quacks like a duck, it must be some kind of duck, may be regarded as involving a sort of measurement process or set of tests ( see duck test ).

Similarly, the " species of partitions " can be defined by assigning to each finite set the set of all its partitions, and the " power set species " assigns to each finite set its power set.

Similarly, any set with 4 elements can be given two non-isomorphic group structures: one isomorphic to ; the other isomorphic to.

Similarly, when Joan reveals her plan to turn Burgundy against the English, Alençon declares, " We'll set thy statute in some holy place / And have thee reverenced like a blessed saint " ( 3. 3. 14 – 15 ).

Similarly experience itself can be conventionalized so that people react to certain preconceived clues for behavior without awareness of the vitality of their experiential field.

Similarly, higher levels of GNP do not, in themselves, provide grounds for raising prices, but they do relax some of the pressure on the industry so that it can raise prices higher for a given wage increase.

Similarly, a character can find any possible universe, but they can spend character points to know of or inhabit shadows which are ( in some sense ) " real " and therefore useful.

Similarly, coral, petrified wood and other organic remains or porous rocks can also become agatized.

Similarly, no one identifies themselves as Amur Valley Ainu, although people with partial descent can be found in Khabarovsk.

Only then in fact was payment for assembly attendance, the central event of democracy ( Similarly for the period before the Persian wars, but for the very early democracy the sources are very meagre and it can be thought of as being in an embryonic state ).

Similarly, Hindi-Urdu speakers might unconsciously apply their native ' v-w ' allophony rules to English words, pronouncing war as var or advance as adwance, which can result in intelligibility problems with native English speakers.

Similarly, intuitionists object to the existence property for classical logic, where one can prove, without being able to produce any term of which holds.

Similarly, the angle that a line makes with the horizontal can be defined by the formula

Similarly, the total mass inside a sphere containing a black hole can be found by using the gravitational analog of Gauss's law, the ADM mass, far away from the black hole.

Similarly, diamond dust used as an abrasive can do harm if ingested or inhaled.

Similarly, one declarative sentence can refer to many propositions ; for instance, " I am hungry " changes meaning ( i. e. refers to different propositions ) depending on the person uttering it.

Similarly, the compiler can be told on a per-module or per-function basis which type safety level is wanted, using optimize declarations.

Similarly, some minor products can be placed below the arrow, often with a minus sign.

Similarly, dry cement powder in contact with mucous membranes can cause severe eye or respiratory irritation.

Similarly, in 1961, Maquet notes that the society in Rwanda and Burundi can be best described as castes.

Similarly, in three dimensions, the vector from the origin to the point with Cartesian coordinates can be written as:

Similarly, we can show that the coefficient of the second term can be substituted by.

Similarly, Lubumbashi and the rest of Katanga Province is linked to Zambia, through which the paved highway and rail networks of Southern Africa can be accessed.

Similarly, a deeper understanding of developmental biology can foster greater progress in the treatment of congenital disorders and diseases, e. g. studying human sex determination can lead to treatment for disorders such as congenital adrenal hyperplasia.

Similarly, it can be shown that the IDFT formula leads to a periodic extension.