Examples of algebraic integers are,, and ( Note, therefore, that the algebraic integers constitute a proper superset of the integers, as the latter are the roots of monic polynomials for all

Note that congruences alter some properties, such as location and orientation, but leave others unchanged, like distance and angle s. The latter sort of properties are called invariant ( mathematics ) | invariant s and studying them is the essence of geometry.

Note the latter is now called Pope Stephen VI.

Note the latter is now called Pope Stephen VI.

Note that in a few cases the accidental might change the note by more than a semitone: for example, if a G sharp is followed in the same measure by a G flat, the flat sign on the latter note means it will be two semitones lower than if no accidental were present.

Note that the definition is somewhat ambiguous because the user of a program can be another program and, if the latter is a portion of the set of program that is required to be interoperable, it might well be that it does need to have knowledge of the characteristics of other units.

Jordan was the first artist to be signed by Bruce Lundvall when the latter became president of Blue Note Records in 1985 and, consequently, Magic Touch was the first release ( not reissue ) of the rejuvenated label.

Note, for example, that the time zone GMT + 14 will be at the same time of day as GMT − 10, though the former is one day ahead of the latter.

Note that differs from dental in that the former is a sibilant and the latter is not.

Note that the verb " see " can often be used instead of " call ": " Bob saw Carol's bet ", although the latter can also be used with the bettor as the object: " I'll see you " means ' I will call your bet '.

( Note: " plebeian secession " was a tactic used by the Roman plebs of vacating a city entirely and leaving its ruling elite to fend for itself, thus an even more radical action than a " general strike ", yet unlike the latter term, it does not pertain to withholding labor within a wage-system.

The second Blue Note session in 1951 was a trio with Russell and Roach, and includes " Parisian Thoroughfare " and " Un Poco Loco ", the latter of which was selected by literary critic Harold Bloom for inclusion on his short list of the greatest works of twentieth-century American art.

Note that part of that profit results from turning the company around, and part results from the general increase in share prices in a buoyant stockmarket, the latter often being the greater component.

Note the payoff of the latter portfolio is also S ( T )-K at time T, since our share bought for S ( t ) will be worth S ( T ) and the borrowed bonds will be worth K.

( Note that the latter term can also mean the original blazar and not the entire class.

Note that the latter is characterized by undesirable scheduling starvation.

Note, however, that PFA can be combined with mixed-radix Cooley – Tukey, with the former factorizing N into relatively prime components and the latter handling repeated factors.

New York is home to several major jazz clubs, including Birdland, Sweet Rhythm ( formerly Sweet Basil ), Village Vanguard and The Blue Note, the latter being one of the premier spots for jazz lovers.

: Note: In this article, to distinguish between the Han state of the Warring States Period and the Han Dynasty, the former will be referred to as " Hán " while " Han " will be reserved for the latter.

Note that webbing construction is either utterly flat or flat-tubular ; the latter tends to handle better but knots are more likely to jam.

Note that this latter form is the functional equation for the Riemann zeta function, as originally given by Riemann.

Note the asymmetry in this latter definition ; which talks about a correspondence from X to Y rather than a correspondence between X and Y.

( Note that this is only used to read and send e-mail, not to create or manage your mail. i2p account ; the latter must be done at hq. postman. i2p.

Note that the latter two structures extend the application of these principles beyond mere completeness requirements by introducing an additional operation of negation.

Note that any model of ZF ¬ C is also a model of ZF, so for each of the following statements, there exists a model of ZF in which that statement is true.

Note that " completeness " has a different meaning here than it does in the context of Gödel's first incompleteness theorem, which states that no recursive, consistent set of non-logical axioms of the Theory of Arithmetic is complete, in the sense that there will always exist an arithmetic statement such that neither nor can be proved from the given set of axioms.

Note also that the terms are not always treated as mutually exclusive ; there is not necessarily anything contradictory in the statement that " the language of the Pennsylvania Dutch is a dialect of German ".

Note that this statement is only true when the refractive indices of both materials are real numbers, as is the case for materials like air and glass.

The Preliminary Note of Explanation did not in fact alter the value of the statement on collegiality in the text of Lumen Gentium: it " strengthened the adherence to the doctrine of the First Vatican Council on the primacy, but it did not subsequently strike out anything from the direct divine origin of the episcopal office and its function, and the responsibility of the College of Bishops for the Universal Church.

Note however that a sentence reflecting a supposed understanding of the actions of others, such as one that contains a statement like " he or she never believed ..." or " those others " is already stepping outside of the solipsist's subjective viewpoint, and so misleading when used to illustrate a solipsistic view of death.

Note: despite the statement in the show that teleportation is a major drain of his energy, when Ultraman teleported from Planet R to Earth his warning light was still blue, and this was also after having destroyed Baltans on Planet R.

Note that for this statement to be true, k must be a constant, or else the k can't be taken outside the limit in the line marked (*).

The Demand Notes ' printed promise of payment " On Demand " was removed and the statement " This Note is a Legal Tender " was added.

Note that if C does not terminate, then there is no " after ", so Q can be any statement at all.

Some such books include a separate ' Note about the type ', which will identify the names of the primary typefaces used, provide a brief description of the type's history and a brief statement about its most identifiable physical characteristics.

Note also that although applications almost always deal with convergence of sequences, the statement is purely algebraic and will work in any field.

Note that the form of statement used in Oberon-2 is unrelated to the Pascal and Modula-2 WITH statement.

Note that a single counterexample falsifies a universally quantified statement, and a single example suffices to verify an existentially quantified one.

( Note: the aforementioned statement is not verified in the documentary " Nazi America: A Secret History ".

Note that there is no POKE statement in TI BASIC.

Note that if " Samuel Clemens " is put into ( 1 ) in place of " Mark Twain ", the result is as true as the original statement.

Then a finer statement of the s-cobordism theorem is that the isomorphism classes of this category ( up to Cat-isomorphism of h-cobordisms ) are torsors for the respective < ref > Note that identifying the Whitehead groups of the various manifolds requires that one choose base points and a path in W connecting them .</ ref > Whitehead groups Wh ( π ), where

Note that the two separate statements may have different semantics ( especially with respect to statement triggers ) and may not provide the same performance as a single multi-row insert.

Note that this is not a valid SQL statement according to the SQL standard ( SQL: 2003 ) due to the incomplete subselect clause.

Note that this construction can be improved by converting some cases of the selection statement into subprocedures.

Note that in this last statement, the series could still be conditionally convergent ; for real-valued series, this could happen if the a < sub > n </ sub > are not all nonnegative.

The statement of payment is formatted the same and surrounded by the same engraved object as the $ 10 Demand Note and is located in the center of the note under the figure of Liberty.