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Hence, the axiom of regularity is equivalent, given the axiom of dependent choice, to the alternative axiom that there are no downward infinite membership chains.
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Hence and axiom
Hence S breaks up into uncountably many orbits under G. Using the axiom of choice, we could pick a single point from each orbit, obtaining an uncountable subset X of S with the property that all of its translates by G are disjoint from X.
Now it is easy to convince oneself that the set X could not possibly be measurable for any rotation-invariant countably additive finite measure on S. Hence one couldn't expect to find an algorithm to find a point in each orbit, without using the axiom of choice.
Hence the ordered pair can be taken as a primitive notion, whose associated axiom is the characteristic property.
Hence S breaks up into uncountably many orbits under G. Using the axiom of choice, we could pick a single point from each orbit, obtaining an uncountable subset with the property that all of its translates by G are disjoint from X and from each other.
" Hence the peripatetic axiom.
" Hence this axiom could have been named " Congruence is Euclidean.
Hence and is
Hence the prime issue, as I see it, is whether a democratic or free society can master technology for the benefit of mankind, or whether technology will rule and develop its own society compatible with its own needs as a force of nature.
Hence government must establish greater controls upon corporations so that their activities promote what is deemed essential to the national interest.
Hence, the only defensible procedure is to repress any and every notion, unless it gives evidence that it is perfectly safe.
Hence the natural setting of tragedy is the palace gate, the public square, or the court chamber.
Hence, the condition of freedom is a necessary condition for choice.
Hence it is difficult to conceive of a packing of the atoms in this material in which the oxygen atoms are far from geometrical equivalence.
Hence the minimal polynomial for Af is Af.
Hence the totality of singular lines is the T order complex of lines which meet Aj.
Hence, thought of as a line in a particular plane **yp, any tangent to Q has a unique image and moreover this image is the same for all planes through L.
Hence C' is a Af curve on Q.
Hence, when the address Af is computed from Af, the cell Af and all Y-cells in its chain must be inspected to determine whether Af is already in the form list or whether it should be added to the form list and the chain.
Hence, the Af factor for the output fiber coupler is Af.
Hence P is the increase in value of the stream minus the cost of operation, that is, the net profit.
Hence, if what is in question is whether in a given theology myth is or is not completely rejected, it is unimportant whether only a little bit of myth or a considerable quantity is accepted ; ;
Hence he was in his lifetime, as is the memory of him afterwards, a canker within the liberal sensitivity.
Hence, such an appellate court will not consider an appellant's argument if it is based on a theory that is raised for the first time in the appeal.
Hence and equivalent
Hence the expression praeteriti senatores (" senators passed over ") is equivalent to e senatu ejecti ( those removed from the senate ).</ br > In some cases, however, the censors did not acquiesce to this simple mode of proceeding, but addressed the senator whom they had noted, and publicly reprimanded him for his conduct.
Hence a grapheme can be regarded as an abstraction of a collection of glyphs that are all semantically equivalent.
Hence, the Shakespeare quote above is semantically distributive, because there's not a man who ... is logically equivalent to every man does not ....
Hence Rel is equivalent to a full subcategory of the category Sup of complete lattices and their sup-preserving maps.
Hence the certainty equivalent is 40.
Hence, the two are not equivalent.
Hence, any two systems moving without acceleration are equivalent, and unaccelerated motion is relative.
Hence, if a circuit has n signal lines, there are potentially 2n stuck-at faults defined on the circuit, of which some can be viewed as being equivalent to others.
" Hence in christological and doctrinal reference " mainstream Christianity " is often equivalent to " Trinitarianism.
Hence representations are equivalent to left C-modules.
Hence, an infantry brigade could consist of three battalions of infantry, but a cavalry brigade of equivalent size would have three regiments.
Hence, as the leaky bucket as a meter and token bucket are equivalent, the leaky bucket as a queue for variable packet lengths is also a special case of a traffic shaping function using a leaky bucket ( or token bucket ) as a meter.
Hence, virtual education is considered by many to be equivalent to a directed-learning program.
Hence, because of the EU's decision to accept Kyoto-CERs as equivalent to EU-EUA's, it is possible to trade EUA's and UNFCCC-validated CERs on a one-to-one basis within the same system.
Hence, the equivalent resistance is
Hence and given
Hence all teachers, good and bad, who have been teaching for a given number of years are paid the same salary.
Hence it is the atomic number alone that determines the chemical properties of an element ; and it is for this reason that an element can be defined as consisting of any mixture of atoms with a given atomic number.
Hence, thicker yarns generally require fewer stitches, and therefore less time, to work up a given project.
Hence the cinemas were given over to imported films, particularly American ones.
Hence, thicker yarns generally require fewer stitches, and therefore less time, to knit up a given garment.
Hence, at any given level in the inheritance chain, there can be at most one implementation of any method.
Hence it does not follow that a thing is not in motion in a given time, just because it is not in motion in any instant of that time.
Hence, in the philosophy of mathematics, the abstraction of actual infinity involves the acceptance of infinite entities, such as the set of all natural numbers or an infinite sequence of rational numbers, as given objects.
Hence, it must be given a meaning of the same kind as the word of established meaning.
Hence, within a field of intellectual enquiry, the practitioners occasionally debate “ What is ” and “ What is not ” discourse, according to the conceptual meanings ( denotation and connotation ) used in the given field of study.
Hence, no canonical source has given any family names to any Vulcan characters, and indeed, every one of the personal names previously mentioned are all officially described as being only Latin-alphabetical and English-phonetic approximations of the real ones.
" Hence, I believe there is only one name that can be given to this car, a name I shall give to it on this very evening.
Hence Catholic writers will sometimes use the term " worship " not to indicate adoration, but only the worship of veneration given to Mary and the saints.
Hence, for a given temperature and pressure, the molar volume is the same for all ideal gases and is known to the same precision as the gas constant: R = 8. 314 4621 ( 75 ) J mol < sup >− 1 </ sup > K < sup >− 1 </ sup >, that is a relative standard uncertainty of 9. 1 × 10 < sup >− 7 </ sup >, according to the 2010 CODATA recommended value.
Hence the phenomenological method relies on the description of phenomena as they are given to consciousness, in their immediacy.
Hence the name Cable Beach given to the landfall site.
Hence, introducing the formal system of logic stops the infinite regression — that is, because the regress would stop at the axioms or rules, per se, of the given game, system, etc.
Hence the existence of models as given by the completeness theorem needs in fact 2 philosophical assumptions: the actual infinity of natural numbers and the consistency of the theory.
Hence, all the WMEs which represent the same entity type typically traverse a given branch of nodes in the discrimination network.
Hence Chalmers half-joking calls for the need to build a " consciousness meter " to ascertain if any given entity, human or robot, is conscious or not.
Hence Catholic writers will sometimes use the term " worship " not to indicate adoration, but only the worship of veneration given to Mary and the saints.
Hence, a great portion of the historical chronicles given in Shahnameh are based on this epic and there are in fact various phrases and words which can be matched between these two sources according to Zabihollah Safa.
Hence criticism is often considered an " art ", because it involves human insight into " what one can say and cannot say " in the given situation.
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