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Page "Axiom of choice" ¶ 6
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Each and choice
Each one is chosen for its aesthetic effect and structural strength, and such choice can also play a significant role in determining the instrument's timbre.
Norwegian has two standards, Bokmål and Nynorsk, the choice between which is subject to controversy: Each Norwegian municipality can declare one of the two its official language, or it can remain " language neutral ".
Each has its pros and cons, so the choice is dependent solely on the individual brewer's preferences.
Each subject was presented with the evidence of guilt and offered a choice between facing an academic ethics board and potentially a heavy penalty in terms of extra courses and other forfeits, or admitting guilt and accepting a lighter " sentence ".
# Each legal category has one or more choice of law rules to determine which of the competing laws should be applied to each issue.
Each coordinate system is named for its choice of fundamental plane.
Each celebrity was given a choice of three adjectives, and the contestant guessed who picked what at $ 100 per match.
Each of the band members is also active in fundraising for a charity of his choice, and several of them have set up their own charitable foundations.
His view has been shared by other historians, for example, Paul Kennedy, who says of the choices facing politicians at the time, " Each course brought its share of disadvantages: there was only a choice of evils.
Each of these preliminary concepts is a potential design choice.
Rawls believes that this principle would be a rational choice for the representatives in the original position for the following reason: Each member of society has an equal claim on their society ’ s goods.
Each such choice of norms gives rise to an operator norm and therefore yields a norm on the space of all m-by-n matrices.
Each one of these " little choices will reveal itself under analysis as the choice of a means towards a predetermined end.
Each team may wear its first choice kit ; however, if these clash the previous year's Europa League winning team must wear an alternative color.
Each repeater included a base station-controlled cross-over data switch to swap traffic through a choice of two fibre pairs, the switch connections in successive repeaters enabled any desired connection to be made and provide a diversity path when required.
Each generation has the choice to overrule or add to the fundamental principles enunciated by the Framers ; the Constitution can be amended or it can be ignored .”
Two episodes at the turn of the calendar year are reserved for “ The McLaughlin Group 19XX / 20XX Year-End Awards .” Each panelist announces his or her choice for each category such as “ Biggest Winner of 2008 ,” ” Best Politician ,” “ Most Boring ,” “ Turncoat of the Year ,” “ Enough Already ,” “ Most Underrated ,” etc., followed by McLaughlin ’ s choice.
Each Contracting Authority issues notices in the language of their choice.
The elements of the quotient group R / Q partition R. There are uncountably many elements, and each element is dense in R. Each element of R / Q intersects 1, and the axiom of choice guarantees the existence of a subset of 1 containing exactly one representative out of each element of R / Q.
Each is specified by a choice of the function K of two variables, the kernel function or nucleus of the transform.
Each contestant selected a category before each spin and received $ 100 if the wheel stopped on their choice.
Each played for a different prize, and was offered a choice of five envelopes containing questions ; a player would have to answer two of three correctly to win the prize.
Each voter encrypts their choice before casting their vote.

Each and function
Each gate consisted of one inverting vacuum tube amplifier, preceded by a resistor divider input network that defined the logical function.
Each isomer is a local minimum on the energy surface ( called the potential energy surface ) created from the total energy ( i. e., the electronic energy, plus the repulsion energy between the nuclei ) as a function of the coordinates of all the nuclei.
Each replacement results in a function taking exactly one argument.
Each is a complex number that encodes both amplitude and phase of a sinusoidal component of function.
Each equivalence relation has a canonical projection map, the surjective function from to given by.
Each tool-design thus acts somewhat similarly to a biological gene in that some populations have it and others do not, and the meme's function directly affects the presence of the design in future generations.
Each stage may have a distinct physiological function and this can result in sleep that exhibits loss of consciousness but does not fulfill its physiological functions ( i. e., one may still feel tired after apparently sufficient sleep ).
Each ensemble is associated with a partition function that, with mathematical manipulation, can be used to extract values of thermodynamic properties of the system.
Each individual list represents one environment level: the parameters of the current function are in the head of the list, variables that are free in the current function, but bound by a surrounding function, are in other elements of E.
Each entry in this sequence needs to be an application of a basic function or follow from the entries above by using composition, primitive recursion or mu recursion.
Each performs a different function, fine-tuning how the wakeboard rides through the water according to its width from tip to tail, fin setup, rocker and tip and tail shape.
* The procedure: Each sample value is multiplied by the sinc function scaled so that the zero-crossings of the sinc function occur at the sampling instants and that the sinc function's central point is shifted to the time of that sample, nT.
Each logic gate represents a function of boolean logic.
Each realisation of a random function would result in a different function.
Each function maps the same temperature value to a truth value in the 0 to 1 range.
Each real set, function, and relation has its natural hyperreal extension, satisfying the same first-order properties.
Each realization is a sample of the complete-dimensional joint distribution function
Each value of the function is usually expressed as a complex number ( called complex amplitude ) that can be interpreted as a magnitude and a phase component.
Each of the Fatou domains contains at least one critical point of, that is, a ( finite ) point z satisfying, or z = ∞, if the degree of the numerator is at least two larger than the degree of the denominator, or if for some c and a rational function satisfying this condition.
Each of these mutations alters the gene's protein product ( i. e., the enzyme ), sometimes severely inhibiting its function .< ref > In recent years, population studies and pedigree analysis have shown how such mutations arise and spread within small founder populations.

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