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It is not a true ordering because the trichotomy law need not hold: if both and, it is true by the Cantor – Bernstein – Schroeder theorem that i. e. A and B are equinumerous, but they do not have to be literally equal ; that at least one case holds turns out to be equivalent to the Axiom of choice.
Some Related Sentences
is and true
The true artist is like one of those scientists who, from a single bone can reconstruct an animal's entire body.
That is particularly true of sovereignty when it is applied to democratic societies, in which `` popular '' sovereignty is said to exist, and in federal nations, in which the jobs of government are split.
On Fridays, the day when many Persians relax with poetry, talk, and a samovar, people do not, it is true, stream into Chehel Sotun -- a pavilion and garden built by Shah Abbas 2, in the seventeenth century -- but they do retire into hundreds of pavilions throughout the city and up the river valley, which are smaller, more humble copies of the former.
The resulting picture might appear a maze of restless confusions and contradictions, but it is more true to life than a portrait of an artificially contrived order.
that is, he is suspect, guilty, punishable, as is anyone in Mann's stories who produces illusion, and this is true even though the constant elements of the artist-nature, technique, magic, guilt and suffering, are divided in this story between Jacoby and Lautner.
A broader concept of imitation is needed, one which acknowledges that true invention is important, that the artist's creativity in part transcends the non-artistic causal factors out of which it arises.
It is true that New England, more than any other section, was dedicated to education from the start.
Though it centers around the brilliant and enigmatic figure of Charles 12,, the true hero is not finally the king himself.
Years ago this was true, but with the replacement of wires or runners by radio and radar ( and perhaps television ), these restrictions have disappeared and now again too much is heard.
is and ordering
Moreover, it is too readily forgotten that in the Republic what gave the initial impetus to Plato's excursus into the construction of an imaginary commonwealth with its ruling-class communism of goods, wives, and children, was his quest for a canon for the proper ordering of the individual human psyche ; ;
The concern of Utopia is with the optimo reipublicae statu, the best ordering of a civil society ; ;
and it is again and again made clear that Utopian communism provides the institutional array indispensible to that best ordering.
Alphabets often come to be associated with a standard ordering of their letters, which can then be used for purposes of collation – namely for the listing of words and other items in what is called alphabetical order.
The basic ordering of the Latin alphabet ( ABCDEFGHIJKLMNOPQRSTUVWXYZ ) is well established, although languages using this alphabet have different conventions for their treatment of modified letters ( such as the French é, à, and ô ) and of certain combinations of letters ( multigraphs ).
This placement is consistent with the modern practice of ordering the elements by proton number, Z, but this number was not known or suspected at the time.
The reason that we are able to choose least elements from subsets of the natural numbers is the fact that the natural numbers are well-ordered: every nonempty subset of the natural numbers has a unique least element under the natural ordering.
One might say, " Even though the usual ordering of the real numbers does not work, it may be possible to find a different ordering of the real numbers which is a well-ordering.
Anaxagoras is famous for introducing the cosmological concept of Nous ( mind ), as an ordering force.
He is noted for ordering the first recorded local expulsion of Jews, when he did so in Poitou in 1249.
* 2009 – Former Peruvian President Alberto Fujimori is sentenced to 25 years in prison for ordering killings and kidnappings by security forces.
( Expressed more technically, in each case the pair ( m, n ) decreases in the lexicographic order on pairs, which is a well-ordering, just like the ordering of single non-negative integers ; this means one cannot go down in the ordering infinitely many times in succession.
The Jewish ordering of the canon suggests that Chronicles is a summary of the entire span of history to the time it was written.
In the Christian ordering, the grouping of the Prophetic Books is the last section of the Old Testament, making Malachi the last book before the New Testament.
A further distinction is sometimes made in the ordering of the letters, to represent the order of the episodes, where the patient's normal state is euthymic, interrupted by episodes of mania followed by depression ( MD ) or vice versa ( DM ).
< cite id = disputedinjunction > The Vatican archives contain an unsigned copy of a more strongly worded formal injunction purporting to have been served on Galileo shortly after Bellarmine's admonition, ordering him " not to hold, teach, or defend " the condemned doctrine " in any way whatever, either orally or in writing ", and threatening him with imprisonment if he refused to obey .</ cite > However, whether this injunction was ever properly served on Galileo is a subject of much scholarly disagreement.
By the well ordering principle, if there are positive integers that satisfy a given property, then there is a smallest positive integer that satisfies that property ; therefore, there is a smallest positive integer satisfying the property " not definable in under eleven words ".
Chromium is remarkable for its magnetic properties: it is the only elemental solid which shows antiferromagnetic ordering at room temperature ( and below ).
is and because
This is puzzling to an outsider conscious of the classic tradition of liberalism, because it is clear that these Democrats who are left-of-center are at opposite poles from the liberal Jefferson, who held that the best government was the least government.
In fact it has caused us to give serious thought to moving our residence south, because it is not easy for the most objective Southerner to sit calmly by when his host is telling a roomful of people that the only way to deal with Southerners who oppose integration is to send in troops and shoot the bastards down.
Had the situation been reversed, had, for instance, England been the enemy in 1898 because of issues of concern chiefly to New England, there is little doubt that large numbers of Southerners would have happily put on their old Confederate uniforms to fight as allies of Britain.
But it is more than irony: one of the main reasons why nationalism is no longer a tenable concept is because it has spread throughout the planet.
The `` approximate '' is important, because even after the order of the work has been established by the chance method, the result is not inviolable.
Often it is recognized that all the details of the pattern may not be essential to the outcome but, because the pattern was empirically determined and not developed through theoretical understanding, one is never quite certain which behavior elements are effective, and the whole pattern becomes ritualized.
Yet often fear persists because, even with the most rigid ritual, one is never quite free from the uneasy feeling that one might make some mistake or that in every previous execution one had been unaware of the really decisive act.
I knew that a conversation with the author would not settle such questions, because a man is not the same as his writing: in the last analysis, the questions had to be settled by the work itself.
I suggested that one must let it in because it is the truth, but Beckett did not take to the word truth.
That is why the form itself becomes a preoccupation, because it exists as a problem separate from the material it accommodates.
It is worth dwelling in some detail on the crisis of this story, because it brings together a number of characteristic elements and makes of them a curious, riddling compound obscurely but centrally significant for Mann's work.