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, all the statements listed below which require choice or some weaker version thereof for their proof are unprovable in ZF, but since each is provable in ZF plus the axiom of choice, there are models of ZF in which each statement is true.

Similarly in St Peter: " Christ .. Who verily was foreordained before the foundation of the world, but was manifest in these last times for you " ( 1 Peter 1: 20 ), and " But the end of all things is at hand " ( 1 Peter 4: 7 ).

Similarly, all output was scrutinized for a Control-D character ( ASCII 4 ), which BASIC programs would send before seemingly PRINTing a disk command to get DOS's attention ( the disk commands would not really get PRINTed but were intercepted by DOS and prevented from making it to the screen output ).

Similarly, and mean that the sum or product is over all prime powers with strictly positive exponent ( so 1 is not counted ):

Similarly, BBC interactive television services all offered a horizontal i-bar along the bottom of television screens, with four colour-coded interactions linked to the four colour buttons on TV remote controls.

Similarly open universities use a blend of technologies and a blend of learning modalities ( face-to-face, distance and hybrid ) all under the rubric of " distance learning.

Similarly, letters of credence may contain the name of the head of state, not the governor-general, even if it is the latter who signs and receives them ; in 2005, Canada, Australia and New Zealand changed their policies and now all letters of credence solely address the governor-general of the relevant nation, not to the sovereign.

Similarly, the 2006-07 celebrations in Edinburgh, Glasgow and Stirling were all cancelled on the day, again due to high winds and heavy rain.

Similarly to Leibniz solution, in a real life, we can say the person ( or any macroscopic object ) is the same, because all signs refer to the person ( or object ) in the past, which evolved in time.

Similarly, almost all of the games utilizing the Id tech 2 engine have Linux ports, the only exceptions being those created by Ion Storm.

Similarly, Samuel Pepys in his diary entry for 15 August 1665 records a dream " that I had my Lady Castlemayne in my arms and was admitted to use all the dalliance I desired with her, and then dreamt that this could not be awake, but that it was only a dream ".

Similarly, virtually all members of LAMP have also resigned from the Louisiana Psychological Association ( LPA ) after many LPA members asserted that the LAMP's prescriptive authority movement secretly came to an agreement with Louisiana's medical board to transfer the practice of psychology for psychologists with prescriptive authority to the medical board.

Similarly, the European Union has placed embargoes on Burma, including an arms embargo, cessation of trade preferences, and suspension of all aid with the exception of humanitarian aid.

" Similarly, all level II bubble universes with different physical constants can in effect be found as " worlds " created by " splits " at the moment of spontaneous symmetry breaking in a level III multiverse.

Similarly GABA acts on several different types of receptors, but all of them have effects ( in adult animals, at least ) that are inhibitory.

Similarly, the principal oboe is considered the leader of the woodwind section, and is the player to whom all others tune.

Similarly, the " Who Controls Our Children " campaign in Pennsylvania claimed that an OBE reform effort was part of a federal program that was " stressing values over academic content, and holding students accountable for goals that are so vague and fuzzy they can't be assessed at all.

Similarly, agnostic atheists reject belief in the existence of all deities, while asserting that whether any such entities exist or not is inherently unknowable.

Similarly, cooked and mashed potatoes or potato flour can be used in the Knödel or dumpling eaten with or added to meat dishes all over central and Eastern Europe, but especially in Bavaria and Luxembourg.

Similarly, IBM wanted a single programming language for all users.

Similarly introduced on the last day of the Congressional session four years later, the Act of March 3, 1855 required the prepayment of postage on all mailings.

Similarly to a classical bit where the state of a transistor in a processor, the magnetization of a surface in a hard disk and the presence of current in a cable can all be used to represent bits in the same computer, an eventual quantum computer is likely to use various combinations of qubits in its design.