While every computable number is definable, the converse is not true: the numeric representations of the Halting problem, Chaitin's constant, the truth set of first order arithmetic, and 0 < sup >#</ sup > are examples of numbers that are definable but not computable.

While with the Naval Ordnance Laboratory he developed an arithmetic element for an electronic digital calculator that he called an " electronic brain.

While weighted means generally behave in a similar fashion to arithmetic means, they do have a few counterintuitive properties, as captured for instance in Simpson's paradox.

While they succeeded in grounding arithmetic in a fashion, it is not at all evident that they did so by purely logical means.

While earlier Greek proofs were largely geometric demonstrations, the development of arithmetic and algebra by Islamic mathematicians allowed more general proofs that no longer depended on geometry.

While Escalante teaches basic arithmetic and elementary and intermediate algebra, he realizes that his students have far more potential.

While the language provides simple matrix operations such as multiplication, the Scilab package also provides a library of high-level operations such as correlation and complex multidimensional arithmetic.

While previous approach focused on " working with specialized ' problems ' in arithmetic ", the emerging structural approach to knowledge had " small children meditating about number theory and ' sets '.

While " pointer " has been used to refer to references in general, it more properly applies to data structures whose interface explicitly allows the pointer to be manipulated ( arithmetically via pointer arithmetic ) as a memory address, as opposed to a magic cookie or capability where this is not possible.

While centered square numbers, like figurate numbers in general, have few if any direct practical applications, they are sometimes studied in recreational mathematics for their elegant geometric and arithmetic properties.

While analogous to ordinary orthogonality, particularly as it is known with ordinary complex number arithmetic, this condition is more subtle.

While usually not included in the above definition of a constraint satisfaction problem, arithmetic equations and inequalities bound the values of the variables they contain and can therefore be considered a form of constraints.

While pointers can be made invalid through a variety of mechanisms, ranging from carrying a null value to out-of-bounds arithmetic to illegal casts to producing them from random integers, a previously-valid reference only becomes invalid in two cases:

While young students learn simple skills such as ways to represent the number of pets belonging to their classmates, or traditional skills such as calculating the arithmetic mean of several numbers, older students might learn concepts that were traditionally neglected, such as the difference between the occasionally dramatic relative risk reduction figures and the more concrete absolute risk reduction, or why political pollsters report the margin of error with their survey results.

While the headmaster taught Latin and Greek, the usher attended to reading, writing, arithmetic and English grammar.

While the mask is off, subjects may be asked to do trivial tasks, such as arithmetic and signing their own name.

While the person issuing it may intend to represent the teachings of Islam accurately, this does not mean that that person's interpretation will gain universal acceptance.

While this remains an unsolved problem for astronomers, it does not necessarily mean that the Lambda-CDM model is completely wrong, but rather that it requires further refinement to accurately reproduce the population of galaxies in the universe.

While for p equal to 0 we assume that it's equal to the geometric mean ( which is, in fact, the limit of means with exponents approaching zero ):

* While the decision problem is NP-complete the optimization problem is NP-hard, its resolution is at least as difficult as the decision problem, and there is no known polynomial algorithm which can tell, given a solution, whether it is optimal ( which would mean that there is no solution with a larger, thus solving the decision problem NP-complete ).

While the constant temperature of the Atlantic Ocean moderates the climate of the south and east coasts of Nova Scotia, heavy ice build-up in the Gulf of Saint Lawrence makes winters colder in northern Nova Scotia ; the shallowness of the Gulf's waters mean that they warm up more than the Atlantic Ocean in the summer, warming the summers in northern Nova Scotia.

While the title states that it is naive, which is usually taken to mean without axioms, the book does introduce all the axioms of Zermelo – Fraenkel set theory and gives correct and rigorous definitions for basic objects.

While the fundamental concepts of PLC programming are common to all manufacturers, differences in I / O addressing, memory organization and instruction sets mean that PLC programs are never perfectly interchangeable between different makers.

While the term two-party system is somewhat imprecise and has been used in different countries to mean different things, there is considerable agreement that a system is considered to be of a two-party nature when election results show consistently that all or nearly all elected officials belong to only one of the two major parties, such as in the United States.

While technically ' bong ' does not mean a device used for smoking mainly marijuana, drug-related connotations have been formed with the word itself ( partly due to punning with Sanskrit bhangah " hemp ").

While revolution is often used as a synonym for rotation, in many fields, particularly astronomy and related fields, revolution, often referred to as orbital revolution for clarity, is used when one body moves around another while rotation is used to mean the movement around an axis.

While conceptually it is mean solar time at 0 ° longitude, precise measurements of the Sun are difficult.

While there was no question that life was present at conception or that it could only become a human being, the thinking was that this did not necessarily mean God had infused the rational, immortal soul into the body at conception.

While it was first thought that this would mean that populations in Europe, India, and Africa had high frequencies of lactase persistence because of a particular mutation, it has now been shown that lactase persistence is caused by several independently occurring mutations.

" While people behave and think in ways that are very disturbing, and that may resemble a disease process ( pain, deterioration, response to various interventions ), this does not mean they actually have a disease.

While part of an intellectual junta that briefly ran Springfield in " They Saved Lisa's Brain ", he proposes plans to limit breeding to once every seven years ( a reference to the Vulcan blood fever of mating, called Pon farr ), commenting that this would mean much less breeding for most, but for him, " much, much more ".

While most thunderstorms move with the mean wind flow through the layer of the troposphere that they occupy, vertical wind shear causes a deviation in their course at a right angle to the wind shear direction.

While Kate was mean to Lizzie in the series, she eventually becomes Lizzie's friend again in The Lizzie McGuire Movie.

While autocephalous does mean self-governing, it literally means " self-headed ".

While the word ecchi could mean anything from mild to insulting in Japanese language, it is used in Western culture to divide between pornography ( hentai ) and playful usage of sexualized imagery ( ecchi ).

While the mean price of houses in the city is $ 459, 833.

While there is some evidence that placebo interventions can alter levels of hormones or endogenous opioids, other prominent components include expectancy effects, regression to the mean, and flawed research methodologies.

While the mean values are taken as predictable variables determined by dynamics laws, the turbulent fluctuations are regarded as stochastic variables.

While it is often difficult to determine who was considered most important on a charter's witness list, placement near the top of the list is usually understood to mean that the signatory was considered important.

While being listed as co-conspirator does not mean that CAIR has been charged with anything, the organization was concerned that the label will forever taint it.

While the pattern is uneven, some having gained more than others, nationalism has in fact served the Western peoples well.

While sovereignty has roots in antiquity, in its present usage it is essentially modern.

While it is hazardous to project the trend of history, it seems clear that a genuine community is painfully emerging in the Western world, particularly among the countries of Western Europe.

While he is worldly, the musician often cultivates public attitudes of childlike astonishment and naivete.

While some think we move too fast and others too slowly, Florida's record is a good one and stands out among the 50.

While white is the coolest summer shade, there are lots of pastel hues along with tintable fabrics that will blend with any wardrobe color.

While it is easy enough to ridicule Hawkins' pronouncement in Pleas Of The Crown from a metaphysical point of view, the concept of the `` oneness '' of a married couple may reflect an abiding belief that the communion between husband and wife is such that their actions are not always to be regarded by the criminal law as if there were no marriage.

While this may well be true in general, I believe it is also important to keep in mind that some recent developments suggest that over the next year or so military electronics may be one of the most strongly growing areas in an economy which is not expanding rapidly in other directions.

While clay is still pressed in mold, press three equally spaced holes 1/4'' '' deep, using pencil eraser, in bottom of clay to allow for proper drying and firing.

While assembled lid is still on design head, gently but firmly press it on plaster board.

While some regression is inevitable, it is discouraged rather than encouraged so that the transference does not follow the stages of planned regression associated with certain casework adaptations of the psychoanalytic model for insight therapy.

While other conditions might be even more effective in bringing about a change from immobility to mobility in Kohnstamm reactivity, it is our hypothesis that all such conditions would have as a common factor the capacity to induce an attitude in the subject which enabled him to divorce himself temporarily from feelings of responsibility for his behavior.

While we had expected that compulsive children in the unstructured school setting would have difficulty when compared to those in the structured, we were surprised to find that the achievement of the high compulsives within the schools where the whole-word method is used in beginning reading compares favorably with that of the low compulsives.

While roleplaying for testing is not too well understood at the present time, it represents one of the major uses of this procedure.

While the phonemes can be very easily stated, no one is likely to be satisfied with the statement until phonemic occurrences can be related in some way to morphemic units, i.e. until the morphophonemics is worked out, or at least far enough that it seems reasonable to expect success.

While the U. S. Department of Labor has a program of projecting industry and occupational employment trends and publishing current outlook statements, there is little tangible evidence that these projections have been used extensively in local curriculum planning.

While it had long been known in general, that `` the public is always wrong '', the use of odd-lot indices now puts the adage on a statistical basis.

While there may be several such industries to which the model of this paper is applicable, the authors make particular claim of relevance to the explanation of the course of wages and prices in the steel industry of the United States since World War 2.

While this influence is a complex matter, depending upon personality factors in the individual as well as upon his social-class experience, there probably are some general statements about social-class background and educational policy that can be made with a fair degree of truth.

While one element is announcing progress, another is delineating its problems.