For theoretical analysis, this approach is more suited for constructing detailed formal proofs and is generally preferred in the research literature.

For instance, a professor of formal logic called Chin Yueh-lin – who was then regarded as China ’ s leading authority on his subject – was induced to write: “ The new philosophy Marxism-Leninism, being scientific, is the supreme truth ”.

For many cytochromes, the metal ion present is that of iron, which interconverts between Fe < sup > 2 +</ sup > ( reduced ) and Fe < sup > 3 +</ sup > ( oxidised ) states ( electron-transfer processes ) or between Fe < sup > 2 +</ sup > ( reduced ) and Fe < sup > 3 +</ sup > ( formal, oxidised ) states ( oxidative processes ).

For example, " the team is in the dressing room " ( formal agreement ) refers to the team as an ensemble, whilst " the team are fighting among themselves " ( notional agreement ) refers to the team as individuals.

For example, while in a conversion to Judaism a convert must accept basic Jewish principles of faith, and renounce all other religions, the process is more like a form of adoption, or changing national citizenship ( i. e. becoming a formal member of the people, or tribe ), with the convert becoming a " child of Abraham and Sarah.

For dance forms without an association structure such as Salsa or Tango Argentino they may not have formal training.

For example, in formal languages like mathematics, a ' stipulative ' definition guides a specific discussion.

For example, in court of justice where strictly formal Thai language is used, Dr cannot be mentioned as a person's title.

For example, Duncan Kennedy, in explicit reference to semiotics and deconstruction procedures, maintains that various legal doctrines are constructed around the binary pairs of opposed concepts, each of which with a claim upon intuitive and formal forms of reasoning that must be made explicit, not only in their meaning but also its relative value, and criticized.

For example, the three members of the Alpha Centauri triple star system are conventionally referred to as Alpha Centauri A, B and C while the formal standard would give their designations as Alpha Centauri Aa, Ab and B respectively.

* K < nowiki ></ nowiki > X < nowiki ></ nowiki >, the ring of formal power series over the field K. For each nonzero power series P, define f ( P ) as the degree of the smallest power of X occurring in P. In particular, for two nonzero power series P and Q, f ( P )≤ f ( Q ) iff P divides Q.

For a history of first-order logic and how it came to be the dominant formal logic, see José Ferreirós 2001.

For much of history and in many cultures, enlisting professional teachers ( whether as tutors or in a formal academic setting ) was an option available only to a small elite.

For a better understanding of the liar paradox, it is useful to write it down in a more formal way.

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

For instance, a major clause must display some structure that is the formal realization of a choice from the system of " voice ", i. e. it must be either " middle " or " effective ", where " effective " leads to the further choice of " operative " ( otherwise known as ' active ') or " receptive " ( otherwise known as " passive ").

For instance, a TOE involving a set of different types of entities ( denoted by words, say ) and relations between them ( denoted by additional words ) is nothing but what mathematicians call a set-theoretical model, and one can generally find a formal system that it is a model of.

For example, the experiments at the PEAR laboratory were criticized in a paper published by the Journal of Parapsychology, in which parapsychologists independent from the PEAR laboratory concluded that these experiments " depart from criteria usually expected in formal scientific experimentation " due to " roblems with regard to randomization, statistical baselines, application of statistical models, agent coding of descriptor lists, feedback to percipients, sensory cues, and precautions against cheating.

For many earlier presidents, however, formal church membership was forestalled until they left office ; and in several cases a president never joined any church.

For each president, the formal affiliation at the time of his presidency is listed first, with other affiliations listed after.

For this reason there was often no reason to write the establishment's name on the sign and inns opened without a formal written name, the name being derived later from the illustration on the pub's sign.

For example are sixth-century objectives, like blending in with contemporary dress or providing service to visitors, better served or compromised by retaining sixth-century clothing or by insisting that service excludes formal educational enterprises?

For a formal exposition of these ideas, see the section Set-theoretic Formulation, below.

For example, Cowboy boots are considered boots, but may also be worn in more formal occasions and used as dress shoes.

Apparently, Jouvet and Ledoux attempted just these dissimilar approaches in the role of Arnolphe in `` The School For Wives ''.

For curves given by the graph of a function, horizontal asymptotes are horizontal lines that the graph of the function approaches as x tends to Vertical asymptotes are vertical lines near which the function grows without bound.

For the proof of the equivalence of the four approaches the reader is referred to mathematical expositions like or.

For example, programming language theory studies approaches to description of computations, while the study of computer programming itself investigates various aspects of the use of programming languages and complex systems, and human-computer interaction focuses on the challenges in making computers and computations useful, usable, and universally accessible to humans.

For example, the perimeter of a regular polygon inscribed in a circle approaches the circumference with increasing numbers of sides ( and decrease in the length of one side ).

For example, programming language theory considers various approaches to the description of computation, whilst the study of computer programming itself investigates various aspects of the use of programming language and complex systems.

For example, German dictionaries and telephone directories use different approaches.

For a " well-behaved " set X, the Hausdorff dimension is the unique number d such that N ( r ) grows as 1 / r < sup > d </ sup > as r approaches zero.

For example, mountain airports such as Reno ( KRNO ) offer significantly different instrument approaches for aircraft landing on the same runway, but from opposite directions.

For systems with subpixels, two different approaches can be taken:

With finite samples, approximation results measure how close a limiting distribution approaches the statistic's sample distribution: For example, with 10, 000 independent samples the normal distribution approximates ( to two digits of accuracy ) the distribution of the sample mean for many population distributions, by the Berry – Esseen theorem.

For pure rocket approaches Tsiolkovsky's rocket equation shows that dead weight will prevent reaching orbit unless the ratio of propellant to structural mass ( called mass ratio ) is very high — between about 10 and 25 ( i. e. 24 parts propellant weight to 1 part structural weight ; depending on propellant choice ).

( For ordinary bradyonic matter, E increases with increasing speed, becoming arbitrarily large as v approaches c, the speed of light ).

For example, in the United States, California's Oakland ( KOAK ), Monterey ( KMRY ) and Santa Ana ( KSNA ) airports routinely grant temporary IFR clearance when a low coastal overcast forces instrument approaches, while the rest of the state is still under visual flight rules.

For large problems, the system poses some unusual difficulties, most notably that problem is never positive definite ( even if is ), making it potentially very difficult to find a good numeric approach, and there are many approaches to choose from dependent on the problem.

For large numbers the Poisson distribution approaches a normal distribution, typically making shot noise in actual observations indistinguishable from true Gaussian noise except when the elementary events ( photons, electrons, etc.

For example, conducting multiple instrument approaches in the actual aircraft may require significant time spent repositioning the aircraft, while in a simulation, as soon as one approach has been completed, the instructor can immediately preposition the simulated aircraft to an ideal ( or less than ideal ) location from which to begin the next approach.

For a philosophy of mathematics that attempts to overcome some of the shortcomings of Quine and Gödel's approaches by taking aspects of each see Penelope Maddy's Realism in Mathematics.

For many optical fiber materials, M ( λ ) approaches zero at a specific wavelength λ < sub > 0 </ sub > between 1. 3 and 1. 5 μm.

For very cold temperatures, heat capacities fall drastically and eventually approach zero as temperature approaches zero.

For a review of several distinct approaches to identifying how law changes that utilize English legal history as a test bed see Robert Palmer, English Legal History course.

For example, conducting multiple instrument approaches in the actual aircraft may require spending a significant amount of time repositioning the aircraft, while in a simulation, as soon as one approach has been completed, the instructor can immediately reposition the simulated aircraft to an ideal ( or less than ideal ) location from which to begin the next approach.

For a pole of the function f ( z ) at point a the function approaches infinity as z approaches a.