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# Topic: Cardinal number

 Cardinal number - Wikipedia, the free encyclopedia In linguistics, cardinal numbers is the name given to number words that are used for quantity (one, two, three), as opposed to ordinal numbers, words that are used for order (first, second, third). In mathematics, cardinal numbers, or cardinals for short, are a generalized kind of number used to denote the size of a set. Cardinality is also an area studied for its own sake as part of set theory, particularly in trying to describe the properties of large cardinals. en.wikipedia.org /wiki/Cardinal_number   (2186 words)

 NationMaster.com - Encyclopedia: Cardinal number   (Site not responding. Last check: 2007-10-22) Cardinal numbers, or cardinals for short, are numbers used to denote the size of a mathematical set. The dignity of cardinal is not an essential part of the legal constitution of the Church; it is a reflection of and participation in the sovereign dignity of the Head of the Church, by the chief clergy of the Church of Rome. As to their civil relations, cardinals were assimilated by the Catholic kings to the rank of princes of the blood royal, cardinals being the highest in the Church, after the pope, just as princes of the blood royal are the first in the kingdom after the king. www.nationmaster.com /encyclopedia/Cardinal-number   (4768 words)

 Cardinal number Info - Encyclopedia WikiWhat.com   (Site not responding. Last check: 2007-10-22) A natural number can be used for two purposes: to describe the size of a set, or to describe the position of an element in a sequence. The position aspect leads to ordinal numbers, which were also discovered by Cantor, while the size aspect is generalized by the cardinal numbers described here. It can also be proved that the cardinal (aleph-0, where aleph is the first letter in the Hebrew alphabet, represented by the Unicode character and#1488;) of the set of natural numbers is the smallest infinite cardinal, i.e., that any infinite set admits a subset of cardinality. www.wikiwhat.com /encyclopedia/c/ca/cardinal_number.html   (1141 words)

 Cardinal - Wikipedia, the free encyclopedia The word cardinal comes from the Latin cardo for "hinge" and usually refers to things of fundamental importance, as in cardinal rule or cardinal sins. Cardinal (Catholicism), a member of the College of Cardinals of the Catholic Church Cardinal, Virginia, a settlement in Mathews County, Virginia en.wikipedia.org /wiki/Cardinal   (186 words)

 cardinal number - Wiktionary Cardinal numbers are generally construed as nouns but function as adjectives. Cardinal numbers may be used as ordinal numbers when followed or preceded by a singular (countable) noun, especially if preceded by the word number or the: Cardinal numbers from 1 to 10 can serve as informal rating description or value, with a scale of 1 to 10 implied; 0 and numbers bigger than 10 are used for hyperbole: en.wiktionary.org /wiki/cardinal_number   (148 words)

 Types of numbers: Cardinal Numbers: Cardinal numbers consider numbers as sets or collections of things that are equinumerous or can be put in a one to one correspondence. Irrational numbers: Numbers that cannot be represented as a ratio of integers. All denumerable infinities are have this cardinal number. www.anselm.edu /homepage/dbanach/31-numbers.htm   (315 words)

 CATHOLIC ENCYCLOPEDIA: Cardinal The cardinals were, therefore, from a very early period, assistants of the pope in his liturgical functions, in the care of the poor, the administration of papal finances and possessions, and the synodal disposition of important matters. Finally, the cardinals were put in charge of several of the great offices of the Church: in the Chancery a cardinal-chancellor or rather vice-chancellor, in the administration of the papal revenues a cardinal-camerarius, in the conduct of the penitentiaria a cardinal-penitentiary. Inimical persecution of a cardinal, personal injury to, or imprisonment of, him, are counted high treason (crimen læsæ majestatis); not only the principals, but also those intellectually responsible for the wrong (originators, participants, auxiliaries), and their male descendants incur the canonical penalties of infamy, confiscation, loss of testamentary rights and civil offices, and excommunication. www.newadvent.org /cathen/03333b.htm   (7811 words)

 PlanetMath: cardinal arithmetic is defined to be the cardinality of the union Cardinal arithmetic obeys many of the same algebraic laws as real arithmetic. This is version 27 of cardinal arithmetic, born on 2004-03-13, modified 2006-05-09. planetmath.org /encyclopedia/CardinalArithmetic.html   (176 words)

 The Arithmetic of Cardinal Numbers Cardinal numbers are simply the equivalence classes under the relation of equipolency. If an infinite number of new customers arrive they also can be accomodated by moving the present occupant of any room, say room i, is moved into room 2i thus freeing up all of the odd numbered rooms for the infinity of new customers. In formulating the notion of a cardinal number as an equivalence class of sets are equipotent; i.e., sets that can be put into a one-to-one correspondence there was the presumption that we could envision a set of all sets and also a set of all sets that are equipotent. www.sjsu.edu /faculty/watkins/cardinals.htm   (1927 words)

 Frege´e;'s Number? Since, probably, counting to numbers as large as the cardinal number of the large herd did not exist at that time, he could still account for all the sheep as follows. Cardinal numbers tell how many things there are in a set, as in "There are four people in my family." If you consider a set and a copy of it, you get two identical sets which are clearly equivalent. The number here is often referred to as the "cardinality" of the set; it is still the cardinal number of the set. www.mathpath.org /concepts/Frege.htm   (1781 words)

 Number Name Rules   (Site not responding. Last check: 2007-10-22) 2b.  The names of the cardinal numbers from twenty (20) through ninety-nine (99) that are not integer multiples of ten (10) are formed by taking the name of the multiple of ten (10) cardinal number and adding a hyphen and the name of the units (1) digit cardinal number. Number Names for the standard English language names for the cardinal numbers from zero through ten thousand (0 through 10,000). See Number Names for the standard English language names for the ordinal numbers from first through ten thousandth (1st through 10,000th). home.comcast.net /~igpl/NWA.html   (589 words)

 Infinite Ink: Cardinal Numbers A cardinal that is not a finite cardinal is an infinite cardinal. In ZF it is possible to have a Dedekind-finite cardinal that is not a finite cardinal. 1 is the ordinal successor of a, is the cardinal successor of aleph www.ii.com /math/cardinals   (1276 words)

 RDEGRAAF.nl [Mathematics: Set Theory and Numbers] In formal set theory, an ordinal number (sometimes simply called an "ordinal" for short) is one of the numbers in Georg Cantor's extension of the whole numbers. In common usage, a cardinal number is a number used in counting (a counting number), such as 1, 2, 3,.... In formal set theory, a cardinal number (also called "the cardinality") is a type of number defined in such a way that any method of counting sets using it gives the same result. www.rdegraaf.nl /index.asp?sND_ID=915157   (491 words)

 cardinal number A number, often called simply a cardinal, that is used to count the objects or ideas in a set or collection: zero, one, two,... For example, it is possible to pair off all the natural numbers with all the even numbers, with none left over; thus the set of natural numbers and the set of even numbers have the same cardinality. Every countable set that is infinite has a cardinality of aleph-null; the set of real numbers has cardinality aleph-one. www.daviddarling.info /encyclopedia/C/cardinal_number.html   (259 words)

 Printable Version on Encyclopedia.com TRANSFINITE NUMBER [transfinite number] cardinal or ordinal number designating the magnitude (power) or order of an infinite set ; the theory of transfinite numbers was introduced by Georg Cantor in 1874. Transfinite ordinal numbers are also defined for certain ordered sets, two such being equivalent if there is a one-to-one correspondence between the sets, which preserves the ordering. The transfinite ordinal number of the positive integers is designated by ω. www.encyclopedia.com /printable.aspx?id=1E1:transfin   (297 words)

 transfinite number ; e.g., the cardinal number 5 may be assigned to each of the sets {1, 2, 3, 4, 5}, {2, 4, 6, 8, 10}, {3, 4, 5, 1, 2}, and { number: The Natural Numbers - The Natural Numbers Cardinal numbers describe the size of a collection of objects; two such... A sequence of numbers, a1, a2, a3, …,... www.factmonster.com /ce6/sci/A0849267.html   (422 words)

 7.8 Random Numbers A random number in some range is chosen in such a way that every number is equally likely to be selected on each occasion. Random numbers generated by formula in a pre-determined sequence are called pseudo-random numbers. It is also worth noting that the last digits of a pseudo-random number sequence cycle through a regular pattern (test this!) and that sequences of random numbers over some specified range that are produced from some generic generator should therefore use the first digits for the numbers in the sequence. www.arjay.bc.ca /Modula-2/Text/Ch7/Ch7.8.html   (2135 words)

 cardinal - Wiktionary a number indicating quantity, or the size of a set, e.g., one, two, three. Of fundamental importance, as in "a cardinal rule". Describing a number used in counting, e.g., one, two, three. en.wiktionary.org /wiki/cardinal   (247 words)

 Do we count from 0 or from 1?   (Site not responding. Last check: 2007-10-22) Note: the definitions 2 of ordinal and cardinal numbers stem from the development of set theory in the 19th century. Any use that depends on the position of the number in the prescribed sequence is the ordinal use of the number. The number found at the top or bottom of a page in a book is an example of the ordinal use of the number. kilby.stanford.edu /~rvg/ordinal.html   (1237 words)

 Large Numbers at MROB   (Site not responding. Last check: 2007-10-22) Cardinal infinity systems are more common in set theory because most set theories have the property that sets are considered equivalent when reordered. Cardinal infinities also occur in topology, geometry and fractal studies because of the practice of treating geometrical objects as "sets" of points. to be the number of countable ordinal infinities. home.earthlink.net /~mrob/pub/largenum-4.html   (2727 words)

 the Counting (Natural) Numbers - the positive integers - the positive whole numbers - the digits Other: Technically, the number zero (naught) is not a part of the Natural Number Set but is important and used in terms of place value. The number "30" is comprised of three groups of size ten and no units. Defn: the number expressing unity or designating a single unit or single item; the lowest cardinal or counting number and the first used in counting a series of objects; a single person, item or thing; the multiplicative identity... www.dsusd.k12.ca.us /users/bobho/counting.htm   (1172 words)

 Example 2.2.7: A Hierarchy of Infinity - Cardinal Numbers   (Site not responding. Last check: 2007-10-22) The cardinal numbers of two sets are equal if the sets are equivalent. Note that according to this definition, we have that the cardinality of the natural numbers is strictly less than the cardinality of the real numbers. If the two sets A and B are disjoint from the outset, one could define the sum of the cardinal numbers as the cardinality of the union of the original sets. www.shu.edu /projects/reals/infinity/answers/cardalg.html   (332 words)

 Transfinite If a set A is finite, there is a nonnegative integer, denoted #A or A, which is the number of elements in A. That number is one of the finite cardinal numbers. If the set is infinite, the corresponding cardinal number is not one of the finite cardinal numbers, so it is called a transfinite (or infinite) cardinal number. Sets having this cardinal number are called countably infinite sets, or just countable sets, because they can be put into one-to-one correspondence with the positive integers, or counting numbers. cs.wwc.edu /KU/Math/Cardinality.html   (708 words)

 Math Forum - Ask Dr. Math As for subtracting infinite cardinal numbers like c-aleph_0, where c is the cardinal of the reals and aleph_0 is the cardinal of the positive integers, I presume that one does it by solving an addition problem: c-aleph_0 = b, where c = aleph_0 + b Then b would have to be c. See the CRC Encyclopedia of Mathematics on Cardinal Numbers (the page is only intermittently available): http://www.astro.virginia.edu/~eww6n/math/CardinalNumber.html "Cardinal Number In informal usage, a cardinal number is a number used in counting (a Counting Number), such as 1, 2, 3,.... Formally, a cardinal number is a type of number defined in such a way that any method of counting Sets using it gives the same result. mathforum.org /library/drmath/view/53370.html   (593 words)

 SIMMER February 1998 Presentation Topic For example, although sqrt(2) is not a rational number, it is an algebraic number, since it is a root of the equation x^2 = 0. The smallest infinite number aleph_0 is the cardinal number of the set N of positive integers. This number is also known as the number of the continuum, because it is the number of all points in the continuum of three-dimensional space. www.math.toronto.edu /mathnet/plain/simmer/topic.feb98.html   (1218 words)

 Ron ButlinVIVALDI, THE JUMPING CARDINAL, GOD, CLINT AND THE NUMBER THREE Cardinal number one, then cardinal number two went leaping over the stone balustrade in a swirl of burgundy-and-scarlet cape. In his imagination he could see the next batch of cardinals jostling to get in line at the rear of the balcony, like so many charter flights waiting for takeoff. A moment later, it, and the jumping cardinal himself, were gone. www.barcelonareview.com /36/e_rb.htm   (1846 words)

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