Help


[permalink] [id link]
+
Page "Algebraic structure" ¶ 65
from Wikipedia
Edit
Promote Demote Fragment Fix

Some Related Sentences

If and all
He said: `` If it's all right with you, Mr. Morgan, I'll sleep out here on the couch.
If, when this was all over, she found the words to tell him about it, she wondered if he would ever understand.
If I hadn't got Nate stopped when I did, my duds'd all be shot plumb to hell!!
`` If Blue Throat has his way he'll keep us all cooped up in here for days '', he said.
If communications work, his decision would be instantly known in all command posts that would originate the actual go order.
If the Union conceded this to them, the same right must be conceded to each remaining state whenever it saw fit to secede: This would destroy the federal balance between it and the states, and in the end sacrifice to the sovereignty of the states all the liberty the citizens had gained by their Union.
If there were only darkness, all would be clear.
If there were only the mess, all would be clear ; ;
If many of the characters in contemporary novels appear to be the bloodless relations of characters in a case history it is because the novelist is often forgetful today that those things that we call character manifest themselves in surface behavior, that the ego is still the executive agency of personality, and that all we know of personality must be discerned through the ego.
If in any one calculation Ptolemy had had to invoke 83 epicycles all at once, while Copernicus never required more than one third this number, then ( in the sense obvious to Margenau ) Ptolemaic astronomy would be simpler than Copernican.
If to be innocent is to be helpless, then I had been -- as are we all -- helpless at the start.
If his scholarship and formal musicianship were not all they might have been, Mercer demonstrated at an early age that he was gifted with a remarkable ear for rhythm and dialect.
If one finger is raised against the authorities, all our moral power will vanish.
If, as Reid says, `` nearly all his poetry was produced when he was not taking opium '', there may be some reason to doubt that he was under its influence in the period from 1896 to 1900 when he was writing the poems to Katie King and making plans for another book of verse.
`` If once they become inattentive to the public affairs '', Jefferson said, `` you and I, and Congress and assemblies, judges and governors, shall all become wolves ''.
If it will simply delay the debates until the qualifications are closed next spring, and then carry all the candidates on a tour of debates, it can provide a service to the state.
If the President of the United States really feels he won himself a `` lousy job '', then heaven help us all.
If we go all gooey over this newest Castro ( until he proves he isn't ) we've got rocks in our heads.
`` If the day should ever come that foreign invaders swarm ashore along the Gulf Coast '', the account reads, `` they can count on heavy opposition from a group of commando-trained telephone employees -- all girls.
If we grasp this orientation as a key, our national conduct in all of the events here mentioned becomes intelligible.
If it is not enough that all of our internationalist One Worlders are advocating that we join this market, I refer you to an article in the New York Times' magazine section ( Nov. 12, 1961 ), by Mr. Eric Johnston, entitled `` We Must Join The Common Market ''.
If Joe doesn't show up, we'll all be back here at 0600 hours.
If we could use all the small airfields we have in this country, we could disperse our strategic aircraft by a factor of 10 or more.
If the points aren't thrown all the way, the Turnout cannot be locked, and in turn, the signal cannot be cleared.
If you have a 6- to 8-inch drain pipe, you may easily wash out all the debris when the grate is out.

If and axioms
If some specific deductive system of first-order logic is sound and complete, then is it " perfect " ( a formula is provable iff it is a semantic consequence of the axioms ), thus equivalent to any other deductive system with the same quality ( any proof in one system can be converted into the other ).
If F is equipped with the order topology arising from the total order ≤, then the axioms guarantee that the operations + and * are continuous, so that F is a topological field.
In universal algebra, a subalgebra of an algebra A is a subset S of A that also has the structure of an algebra of the same type when the algebraic operations are restricted to S. If the axioms of a kind of algebraic structure is described by equational laws, as is typically the case in universal algebra, then the only thing that needs to be checked is that S is closed under the operations.
The later invention of non-Euclidean geometry does not resolve this question ; for one might as well ask, " If given the axioms of Riemannian geometry, can an omnipotent being create a triangle whose angles do not add up to more than 180 degrees?
If G were provable under the axioms and rules of inference of T, then T would have a theorem, G, which effectively contradicts itself, and thus the theory T would be inconsistent.
If these requirements are not met, it's not possible to interpret the wavefunction as a probability amplitude ; the values of the wavefunction and its first order derivatives may not be finite and definite ( with exactly one value ), i. e. probabilities can be infinite and multiple-valued at any one position and time-which is nonsense, as it does not satisfy the probability axioms.
If CP is combined with time reversal ( T-symmetry ), the resulting CPT-symmetry can be shown using only the Wightman axioms to be universally obeyed.
If one considers a generalization of the Wightman axioms to dimensions other than 4, this ( anti ) commutativity postulate rules out anyons and braid statistics in lower dimensions.
To elaborate this message, Holmes first turned to the distinction between law and morals: “ The prophecies of what the courts will do in fact, and nothing more pretentious, are what I mean by the law .” If law is prophecy, Holmes continues, we must reject the view of “ text writers ” who tell you that law “ is something different from what is decided by the courts of Massachusetts or England, that it is a system of reason that is a deduction from principles of ethics or admitted axioms or what not, which may or may not coincide with the decisions .” Holmes next introduces his most important and influential argument, the “ bad-man ” theory of law: “ f we take the view of our friend the bad man we shall find that he does not care two straws ” about either the morality or the logic of the law.
If j is the elementary embedding mentioned in one of these axioms and κ is its critical point, then λ is the limit of as n goes to ω.
If the second axiom, that of idempotence, is relaxed, then the axioms define a preclosure operator.
If one defines a homology theory axiomatically ( via the Eilenberg-Steenrod axioms ), and then relaxes one of the axioms ( the dimension axiom ), one obtains a generalized theory, called an extraordinary homology theory.
Skolem also pointed out that a consequence of the Löwenheim – Skolem theorem is what is now known as Skolem's paradox: If Zermelo's axioms are consistent, then they must be satisfiable within a countable domain, even though they prove the existence of uncountable sets.
Ifis interpreted as the interior operator of topology, ( 1 )-( 3 ) above plus the axiom ∀(∀ x ) = ∀ x make up the axioms for an interior algebra.
Action axioms are of the form " If a condition holds, then the following should be done ".
If this pair of axioms describe all the ways in which fluent can change value, they can be rewritten as a single axiom:
If a set of axioms is D-Complete, then any vaild theorems of the system can be generated by condensed detachment alone.
If the scope of all quantified variables in the above axioms is restricted to sets, all axioms except III and the schema IV are ZFC axioms.
* If after applying a resolution rule the empty clause is derived, the original formula is unsatisfiable ( or contradictory ), and hence it can be concluded that the initial conjecture follows from the axioms.

0.245 seconds.