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For example, the axiom AC < sub > 11 </ sub > can be paraphrased to say that for any relation R on the set of real numbers, if you have proved that for each real number x there is a real number y such that R ( x, y ) holds, then there is actually a function F such that R ( x, F ( x )) holds for all real numbers.
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For and example
For the family is the simplest example of just such a unit, composed of people, which gives us both some immunity from, and a way of dealing with, other people.
For example, suppose a man wearing a $200 watch, driving a 1959 Rolls Royce, stops to ask a man on the sidewalk, `` What time is it ''??
For example, there are persons who are in physical science, in the field of mineralogy, trained in crystallography, who use only X-rays, applying only the powder technique of X-ray diffraction, to clay minerals only, and who have spent the last fifteen years concentrating on the montmorillonites ; ;
For example, No. 56 printed the patent giving the Electoral Prince the title of Duke of Cambridge.
For example, he captured some persons from York County, who with teams were taking to Philadelphia the furniture of a man who had just been released from prison through the efforts of his wife, and who apparently was helpless to prevent the theft of his household goods.
For example, even the most successful executive lives in a two-room apartment while ordinary people rent space in the stairwells of office buildings in which to sleep at night ; ;
For example, in the third chapter of Matthew, verses 13-16, describing the baptism of Jesus, the 1611 version reads:
For example: 1.
For example, it probably will be necessary for the Corps to have authority to pay medical expenses of volunteers.
For example, the importance of the Regulus 2, a very promising aerodynamic ship-to-surface missile designed to be launched by surfaced submarines, was greatly diminished by the successful acceleration of the much more advanced Polaris ballistic missile launched by submerged submarines.
For example, the interest of past members of the Foundation's Advisory Board remains such that they place their knowledge and judgments at our disposal much as they had done when they were, formally, members of that Board.
For example, out of the social evils of the English industrial revolution came the novels of Charles Dickens ; ;
For example, a 12-to-one engine would power a supersonic VTOL fighter.
For example: Af.
For example: Af.
For example, for the problem Af, 10 from 25 equals 15, then 6 from 15 equals 9.
For example: Af.
For example, let's consider a standard 283 cubic inch Chevy Aj.
For an example let's dream up an engine that has a final combustion chamber volume of 5 cubic inches and a cylinder volume of 45 cubic inches.
For example, a Browning trap version of the Superposed over/under, the Broadway ( from $350 up, depending on grade ), differs from standard models in that it is equipped with a full beavertail fore end, a cushion recoil pad and a barrel-wide ventilated rib for fast sighting.
For example, the Chamber of Commerce of Gatlinburg, Tennessee, sponsors special camera tours into the Great Smoky Mountains to get pictures of the profusion of wild flowers flourishing in these wooded regions.
For example, the Friday after Thanksgiving can be substituted for Washington's birthday.
For example, the officials of Poughkeepsie town ( township ) where the project is located think highly of it because it simplifies their snow clearing problem.
For example, don't pay in a truck policy for medical coverage that you may be paying for in a health and accident policy.
For example: If your bodily injury claims start payment after the first $250, a 25% premium saving is often made.
For and axiom
For example for any ( even infinite ) collection of pairs of shoes, one can pick out the left shoe from each pair to obtain an appropriate selection, but for an infinite collection of pairs of socks ( assumed to have no distinguishing features ), such a selection can be obtained only by invoking the axiom of choice.
For finite sets X, the axiom of choice follows from the other axioms of set theory.
For example, while the axiom of choice implies that there is a well-ordering of the real numbers, there are models of set theory with the axiom of choice in which no well-ordering of the reals is definable.
For example, in some groups, the group operation is commutative, and this can be asserted with the introduction of an additional axiom, but without this axiom we can do quite well developing ( the more general ) group theory, and we can even take its negation as an axiom for the study of non-commutative groups.
For example Playfair's axiom states:
For example, Euclid assumed implicitly that any line contains at least two points, but this assumption cannot be proved from the other axioms, and therefore must be an axiom itself.
For example, the direct sum of the R < sub > i </ sub > form an ideal not contained in any such A, but the axiom of choice gives that it is contained in some maximal ideal which is a fortiori prime.
For example the axiom of choice implies that when the size under consideration is the ordinary notion of length for subsets of the real line, then there exist sets for which no size exists, for example, the Vitali sets.
For example, many results about Borel sets are proved by transfinite induction on the ordinal rank of the set ; these ranks are already well-ordered, so the axiom of choice is not needed to well-order them.
For more than a century, Lyell's rhetoric conflating axiom with hypotheses has descended in unmodified form.
For every vector space there exists a basis ( if one assumes the axiom of choice ), and all bases of a vector space have equal cardinality ( see dimension theorem for vector spaces ); as a result the dimension of a vector space is uniquely defined.
For example, the axiom that states " for any number x, x + 0 = x " still applies.
: For the separation axioms in topology, see separation axiom.
For example, the axiom of pairing says that given any two sets a and b there is a new set
This limitation allows statements of the form " for any number x ..." For example, the axiom that states " for any number x, x + 0 = x " would still apply.
For example, the commutativity axiom x + y = y + x holds.
For others, conversely, the axiom of Divine Unity ( see Shema Yisrael ) informs the understanding of Divine Simplicity.
For example, consider the following two instances of the assignment axiom:
For example, compare the semantic clarity of English axiom, Chinese gongli 公理, and Chinglish ( literal translation ) " universal-principle "; median, zhongshu 中数, and " centre-number "; or trapezoid, tixing 梯形, and " ladder-figure ".
For example, in the context of ordered fields, one has the axiom of Archimedes which formulates this property, where the field of real numbers is Archimedean, but that of rational functions in real coefficients is not.
For example, one may define a group as a set with a binary product operator obeying several axioms, including an axiom that the product of any two elements of the group is again an element.
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