What we have done here is arranged the integers and the odd integers into a one-to-one correspondence ( or bijection ), which is a function that maps between two sets such that each element of each set corresponds to a single element in the other set.

An important guide for making these choices is the correspondence principle, which states that the predictions of quantum mechanics reduce to those of classical mechanics when a system moves to higher energies or — equivalently — larger quantum numbers, i. e. whereas a single particle exhibits a degree of randomness, in systems incorporating millions of particles averaging takes over and, at the high energy limit, the statistical probability of random behaviour approaches zero.

It was not until 1956 that Bernhard Bischoff identified a third manuscript ( consisting of a single leaf ) that contained fragments of Fronto's correspondence with Verus, which overlapped the Milan palimpsest ; however, the actual manuscript had been first published in 1750 by Dom Tassin, who conjectured that it might have been the work of Fronto.

The elder Galilei, influenced by his correspondence with Girolamo Mei on the writings of the ancient Greeks and with Erycius Puteanus on the writings of Hucbald and wishing to recreate the old manner of storytelling and drama, pioneered the use of a single melodic line to tell the story, accompanied by simple chords from a harpsichord or lute.

In the first case, the exact one-to-one correspondence may be lost ( for example, some phoneme may be represented by a digraph instead of a single letter ), but the " regularity " is retained, in that there is still an algorithm ( though a more complex one ) for predicting the spelling from the pronunciation and vice versa.

Hiragana and Katagana to Polivanov cyrillization correspondence table, for single / modified kana.

The length of each correspondence ranged from a single card to hundreds sent consecutively over a period of months ; the gesture's repetitive nature is counterbalanced by the artist's peripatetic global wanderings and exceedingly irregular hours ( in 1973 alone he sent postcards from twenty-eight cities ).

" In multiway switching, the correspondence between a single switch's state and whether lights are on or off depends on other switches in the circuit.

The files are arranged alphabetically with publisher correspondence and French author – translation queries and notes all in a single alphabet.

Printed in a book-like page size and using a single-column format, each issue features a single extended essay of at least 20, 000 words, with an introduction by the editor, and correspondence relating to essays in previous issues.

There is a one-room public school, facilitated at the Pictou Island Community Centre, with a single part-time teacher for students up to grade 6, after which students begin correspondence studies.

The city — which in France corresponds to the concept of the " Urban unit " – does not necessarily have a correspondence with a single administrative location, and instead includes other communities that link themselves to the city centre and form the banlieues.

* Temple of Hate: Jerusalem is stormed by an army of the Holy Roman Church, in correspondence with the real event occurring in July 1099, and overcome with their zeal for Christianity, annihilate every single inhabitant.

A single letter of Firmilian to Cyprian survives among Cyprian's correspondence.

These conflicts are documented in a single printed source: the narrative and reprinted correspondence that comprise A Brieff discours off the troubles begonne at Franckford ... A. D. 1554.

Usually, a unicast address is associated with a single device or host, but it is not a one-to-one correspondence.

This is an example of the correspondence principle, the result manifests as Newton's second law in the case of having so many particles that the net motion is given exactly by the expectation value of a single particle.

However, after further correspondence with the Deputy Minister and consultation with their lawyer, Emily Murphy advised the Deputy Minister that they accepted the single question posed by the Cabinet.

It concerns the correspondence of consonants in the older Indo-European, and Low Saxon and High German languages, and was first fully stated by Grimm in the second edition of the first part of his grammar.

Orthographies with a high grapheme-to-phoneme correspondence ( excluding exceptions due to loan words and assimilation ) include those of Finnish, Albanian, Georgian, Turkish ( apart from ğ and various palatal and vowel allophones ), Serbo-Croatian ( Serbian, Croatian and Bosnian ), Bulgarian, Macedonian ( if the apostrophe is counted, though slight inconsistencies may be found ), Eastern Armenian ( apart from o, v ), Basque ( apart from palatalized l, n ), Haitian Creole, Castilian Spanish ( apart from h, x, b / v, and sometimes k, c, g, j, z ), Czech ( apart from ě, ů, y, ý ), Polish ( apart from ó, h, rz ), Romanian ( apart from distinguishing semivowels from vowels ), Ukrainian ( mainly phonemic with some other historical / morphological rules, as well as palatalization ), Swahili ( missing aspirated consonants, which do not occur in all varieties and are sparsely used anyways ), Mongolian ( apart from letters representing multiple sounds depending on front or back vowels, the soft and hard sign, silent letters to indicate / ŋ / from / n / and voiced versus voiceless consonants ) Azerbaijani ( apart from k ), and Kazakh ( apart from и, у, х, щ, ю ).

Unlike Egyptian writing, there was a simple one-to-one correspondence between the two forms of Meroitic, except that in the cursive form, consonants are joined in ligatures to a following vowel i.

Henrietta, however, was at that time engaged in a lengthy correspondence with Joe's older and more serious brother, Morris, who was just about her own age and whom she had got to know well during trips to Philadelphia with Papa, when he substituted for Rabbi Jastrow at Rodeph Shalom Temple there during its Rabbi's absence in Europe.

Another editor pointed despairingly at a bundle of letters that had accumulated for him, saying, `` But Mr. Hearst, what shall I do with this correspondence ''??

Further, he had taken full advantage of the Army's correspondence courses.

Because of his widespread correspondence with others throughout the British Isles, and due to the fact that many of the letters imply that Bede had met his correspondents, it is likely that Bede travelled to some other places, although nothing further about timing or locations can be guessed.

The preface makes it clear that Ceolwulf had requested the earlier copy, and Bede had asked for Ceolwulf's approval ; this correspondence with the king indicates that Bede's monastery had excellent connections among the Northumbrian nobility.

Adolf Hitler's correspondence with his economists also reveals that his intent was to wage war in 1943 – 1945 when the resources of central Europe had been absorbed into the Third Reich.

The letters, part of a larger and somewhat one-sided correspondence in which Heger frequently appears not to have replied, reveal she had been in love with a married man, although they are complex and have been interpreted in numerous ways, including as an example of literary self-dramatisation and an expression of gratitude from a former pupil.

Their correspondence was never published in the media, nonetheless it was sent to Michael Barrier, who had conducted the interview with Clampett and was distributed by Jones to multiple people concerned with animation over the years.

In the United States William Rainey Harper, first president of the University of Chicago developed the concept of extended education, whereby the research university had satellite colleges of education in the wider community, and in 1892 he also encouraged the concept of correspondence school courses to further promote education, an idea that was put into practice by Columbia University.

In one correspondence, Murad entertained the notion that Islam and Protestantism had " much more in common than either did with Roman Catholicism, as both rejected the worship of idols ", and argued for an alliance between England and the Ottoman Empire.

In their early correspondence, Luther expressed boundless admiration for all Erasmus had done in the cause of a sound and reasonable Christianity and urged him to join the Lutheran party.

Science fiction fanzines had their beginnings in Serious & Constructive ( later shortened to sercon ) correspondence.

After two years, he gave up his appointment to pursue his studies at Leipzig, where, as rector, he received the support of the professor of classics, Peter Mosellanus ( 1493 – 1525 ), a celebrated humanist of the time, with whom he had already been in correspondence.

Although the stories of Blaine's favors to the railroads had made the rounds eight years earlier, this time Blaine's correspondence was discovered, making his earlier denials less plausible.

On some of the most damaging correspondence, Blaine had written " Burn this letter ," giving Democrats the last line to their rallying cry: " Blaine, Blaine, James G. Blaine, the continental liar from the state of Maine, ' Burn this letter!

By the end of the Hittite Empire, the Hittite language had become a written language of administration and diplomatic correspondence.

Under the Articles of Confederation, the United States had no executive branch ; the President of Congress was a mostly ceremonial position within the Confederation Congress, but the office did require Hanson to handle a good deal of correspondence and sign official documents.

On his deathbed, Tetzel received a magnanimously penned correspondence from Martin Luther, stating that the child ( i. e. the scandal ) had a different father.

On the evidence of Schwitters ' correspondence, by 1937 it had spread to two rooms of his parents ' apartment on the ground floor, the adjoining balcony, the space below the balcony, one or two rooms of the attic and possibly part of the cellar.

In one correspondence, Murad entertained the notion that Islam and Protestantism had " much more in common than either did with Roman Catholicism, as both rejected the worship of idols ", and argued for an alliance between England and the Ottoman Empire.

Marge Devine Duffy, a secretary in King Features public relations department, had been helping Russell handle correspondence to the NCS, and in 1948, she was installed as the official NCS secretary and later given the title Scribe of the Society.

But any further development of Otho's policy was checked once Otho had read through Galba's private correspondence and realized the extent of the revolution in Germany, where several legions had declared for Vitellius, the commander of the legions on the lower Rhine River, and were already advancing upon Italy.