For proper accreditation of schools, teachers in any course must have a degree at least one level above that for which the student is a candidate.

For purely inertial navigators, two techniques are available to accomplish the platform heading: Use of external or surveying equipment to establish proper heading ; ;

For Euclid ’ s method to succeed, the starting lengths must satisfy two requirements: ( i ) the lengths must not be 0, AND ( ii ) the subtraction must be “ proper ”, a test must guarantee that the smaller of the two numbers is subtracted from the larger ( alternately, the two can be equal so their subtraction yields 0 ).

For a first order predicate calculus, with no (" proper ") axioms, Gödel's completeness theorem states that the theorems ( provable statements ) are exactly the logically valid well-formed formulas, so identifying valid formulas is recursively enumerable: given unbounded resources, any valid formula can eventually be proven.

For example, the class of all sets would be a proper class.

For example, the proper divisors of 6 are 1, 2, and 3.

For example, the smallest pair of amicable numbers is ( 220, 284 ); for the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110, of which the sum is 284 ; and the proper divisors of 284 are 1, 2, 4, 71 and 142, of which the sum is 220.

For this reason, players should choose badminton shoes rather than general trainers or running shoes, because proper badminton shoes will have a very thin sole, lower a person's centre of gravity, and therefore result in fewer injuries.

) For the casuist, the circumstances of a case are essential for evaluating the proper response.

For example, in the 1919 book Chemistry of Human Life physician George W. Carey states that, " Health depends on a proper amount of iron phosphate Fe < sub > 3 </ sub >( PO < sub > 4 </ sub >)< sub > 2 </ sub > in the blood, for the molecules of this salt have chemical affinity for oxygen and carry it to all parts of the organism.

For decades it has been unlikely that a complex information system can be built effectively without a proper database supported by a DBMS.

For molecules of a liquid to evaporate, they must be located near the surface, be moving in the proper direction, and have sufficient kinetic energy to overcome liquid-phase intermolecular forces.

For example if a person is charged with speeding, in a hypothetical case the prosecution has to prove that the person was the driver of the motor vehicle and that it was being driven in excess of the proper speed without any lawful excuse.

Similarly, in regard to passages from the Enneads, " The only space or place of the world is the soul " and " Time must not be assumed to exist outside the soul ", Ludwig Noiré wrote: " For the first time in Western philosophy we find idealism proper in Plotinus, However, Plotinus does not address whether we know external objects, unlike Schopenhauer and other modern philosophers.

For Star Trek III: The Search for Spock ( 1984 ) director Leonard Nimoy and writer-producer Harve Bennett wanted the Klingons to speak a proper language instead of made-up gibberish and so commissioned Okrand to develop the phrases Doohan had come up with into a full language.

If he succeeded and built the Holy Temple in its proper place and gathered the dispersed ones of Israel together, this is indeed the anointed one for certain, and he will mend the entire world to worship the Lord together, as it is stated: " For then I shall turn for the nations a clear tongue, so that they will all procalim the Name of the Lord, and to worship Him with a united resolve ( Zephaniah 3: 9 ).

For instance, the class of all ordinal numbers, and the class of all sets, are proper classes in many formal systems.

For example, Russell's paradox suggests a proof that the class of all sets which do not contain themselves is proper, and the Burali-Forti paradox suggests that the class of all ordinal numbers is proper.

For example, any set theory with a universal set has proper classes which are subclasses of sets.

For example, a non-identity finite group is simple if and only if it is isomorphic to all of its non-identity homomorphic images, a finite group is perfect if and only if it has no normal subgroups of prime index, and a group is imperfect if and only if the derived subgroup is not supplemented by any proper normal subgroup.

For example, Petrarch struggled with the proper relation between the active and contemplative life, and tended to emphasize the importance of solitude and study.

For instance, the normalizer N of a proper subgroup H of a finite p-group G properly contains H, because for any counterexample with H = N, the center Z is contained in N, and so also in H, but then there is a smaller example H / Z whose normalizer in G / Z is N / Z = H / Z, creating an infinite descent.

For proper results, strong flour with high protein content ( as used for bread-making rather than cakes ) must be used.

For the making of selections on the basis of excellence requires that any foundation making the selections shall have available the judgments of a corps of advisors whose judgments are known to be good: such judgments can be known to be good only by the records of those selected, by records made subsequent to their selection over considerable periods of time.

For purposes of sample selection only ( individual tests were given later ) we obtained group test scores of reading achievement and intelligence from school records of the entire third-grade population in each school system.

For almost one-sixth of the national population discrimination in the free selection of residence casts a considerable shadow upon these values assumed as self-evident by most Americans.

For this latest addition to the Great Letters Series, under the general editorship of Louis Kronenberger, Miss Hardwick has made a selection which admirably displays the variety of James's genius, not to mention the felicities of his style.

For example for any ( even infinite ) collection of pairs of shoes, one can pick out the left shoe from each pair to obtain an appropriate selection, but for an infinite collection of pairs of socks ( assumed to have no distinguishing features ), such a selection can be obtained only by invoking the axiom of choice.

For example, antibacterial selection within whole bacterial populations for strains having previously acquired antibacterial-resistance genes was demonstrated in 1943 by the Luria – Delbrück experiment.

For example, Darwinism may be used to refer to Darwin's proposed mechanism of natural selection, in comparison to more recent mechanisms such as genetic drift and gene flow.

Malaria Foundation International states, " The outcome of the treaty is arguably better than the status quo going into the negotiations ... For the first time, there is now an insecticide which is restricted to vector control only, meaning that the selection of resistant mosquitoes will be slower than before.

For example, machines, unlike humans, can support a wide selection of learning algorithms, and controversy has arisen over the relative ethical merits of these options.

With Dewey as the director and his wife as principal, the University of Chicago Laboratory school, was dedicated “ to discover in administration, selection of subject-matter, methods of learning, teaching, and discipline, how a school could become a cooperative community while developing in individuals their own capacities and satisfy their own needs .” ( Cremin, 136 ) For Dewey the two key goals of developing a cooperative community and developing individuals ’ own capacities were not at odds ; they were necessary to each other.

( For example, selection sort requires that the entire list be given before it can sort it, while insertion sort doesn't.

For example, it is the title of a selection of Mormon writings.

For example, the bread-and-butter Soldier class has medium armor, medium speed, and a well-rounded selection of weapons and grenades, while the Scout class is lightly armored, very fast, has a scanner that detects nearby enemies, but has very weak offensive weapons.

For that reason ergometer scores are generally not used as the sole selection criterion for crews, and technique training is limited to the basic body position and movements.

* For a selection of his works with facing French translation: Rodolphe Agricola, Écrits sur la dialectique et l ' humanisme, ed.

For intersexual selection to work, one sex must evolve a feature alluring to the opposite sex, sometimes resulting in a " fashion fad " of intense selection in an arbitrary direction.

For instance, evolution history shows increased neck length not correlated to increases in other parts of the body, which is what would be expected in foraging selection.

For a given physical process, the selection of suitable independent local non-equilibrium macroscopic state variables for the construction of a thermodynamic description calls for qualitative physical understanding, rather than being a simply mathematical problem concerned with a uniquely determined thermodynamic description.

For each election includes good scholarly history and selection of primary documents.

For example the COMMUNITY attribute ( see below ) is not directly used by the BGP selection process.

For example, if only a few closely related males survive a natural disaster, and all are able to mate very widely due to lack of males, sexual selection has been suppressed by an ecological selection ( the disaster ).

For another example, in a region devastated by nuclear radiation, such as the Bikini Atoll, capacity to survive gamma rays to sexual maturity and ( for the female ) to term is a key ecological selection factor, although it is neither " natural " nor sexual.