CO OZNACZA SŁOWO CARDINAL NUMBER
Numer kard
W matematyce, numerach kardynalnych lub kardynałów jest krótkotrwałe uogólnienie naturalnych liczb używanych do pomiaru pojemności zbiorów. Cardinality zbioru skończonego jest liczbą naturalną - liczbą elementów zestawu. Numery kardynalne transfinitów opisują rozmiary nieskończonych zestawów. Kardynalność jest definiowana jako funkcja bijective. Dwa zestawy mają tę samą cardinality, jeśli tylko wtedy, gdy istnieje między nimi bijność. W przypadku skończonych zestawów zgadza się to z intuicyjnym pojęciem wielkości. W przypadku zestawów nieskończonych zachowanie jest bardziej złożone. Podstawowe twierdzenie Georga Cantora wskazuje, że możliwe jest, że nieskończone zestawy mają różne kardiomaty, a zwłaszcza cardinalność zbioru liczb rzeczywistych jest większa niż liczebność zbioru liczb naturalnych. Możliwe jest także, że właściwy podzbiór zbioru nieskończonego ma tę samą cardinalność, co pierwotny zestaw, coś, co nie może się zdarzyć z właściwymi podzbiorami skończonych zbiorów. Istnieje sekwencja transfinitalna numerów kardynalnych: ta sekwencja zaczyna się od liczb naturalnych, w tym zera, po których następuje numer aleph.
Definicja słowa cardinal number w słowniku
Definicja liczby kardynalnej w słowniku to liczba oznaczająca ilość, ale nie kolejność w zbiorze Czasami skrócona do: kardynał. Inna definicja liczby kardynalnej to szczególna liczba posiadająca tę funkcję.
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1
Set Theory and Metric Spaces
We are ready for the general definition. DEFINITION. Let d and e be nonzero
cardinal numbers. Let D and E be sets with o(/>) = d, o(E) = e. We define d* to be
the cardinal number of the set of all functions from E to D. Remark: We have ...
2
Introduction to
Cardinal Arithmetic
Therefore we get Since obviously the cardinality of the index set is at most the
supremum of the summands, Lemma 1.6.3 says that ^<5>^=suP{K^:£</?}<K^. €</
3 Definition Assume that k is an infinite and A is an uncountable cardinal number.
Michael Holz, Karsten Steffens, E. Weitz,
2009
3
An Introduction to Analysis
For this reason, and for others to be elucidated shortly (see Problem D), it is
customary to write 2card* for the cardinal number of the power class on an
arbitrary set X. Thus, in particular, 2N° is the cardinal number of the power class
on N. This ...
Arlen Brown, Carl M. Pearcy,
1995
The cardinal number (or cardinality) of a set A, denoted |A|, is the equivalence
class of A under the equivalence relation of equipollence. \A\ is an infinite or finite
cardinal according as A is an infinite or finite set. Cardinal numbers will also be ...
Thomas W. Hungerford,
1974
5
The Child's Understanding of
Number
Nor do we assume that a child who uses the counting procedure to establish
such a representation has a full appreciation of all the properties of cardinal
number. There are several set-theoretic definitions of cardinal number, which we
will ...
Rochel GELMAN, C. R. Gallistel, Rochel Gelman,
2009
Every finite class has a finite cardinal number, which may be identified with the
number of elements in the class in the ordinary sense; and the finite cardinal
numbers may accordingly be denoted by the symbols 1, 2, . . . . If a finite class is ...
Cardinal number of a set The number of elements in a finite set is called the
cardinal number of the set. The cardinal number is used to denote the size of a
set. If A is any finite set, then its cardinal number is denoted by n(A). For example:
If A= ...
8
Foundations and Fundamental Concepts of Mathematics
FIGURE 8.5 Definition 3 Two sets that are equivalent are said to have the same
cardinal number. All sets that have the same cardinal number as the set {a} are
said to have cardinal number one (or to contain one element); all sets having the
...
9
Elements of the Theory of Functions and Functional Analysis
finite sets the concept of cardinal number coincides simply with the concept of
number of elements in the set. The cardinal number of the set of natural numbers
(i.e. of any denumerable set) is denoted by the symbol Ki (read "aleph xero").
A. N. Kolmogorov, Sergeĭ Vasilʹevich Fomin, S. V. Fomin,
1999
10
Georg Cantor: His Mathematics and Philosophy of the Infinite
managed to establish that the cardinality of Z(K0) was greater than NO, and that
any infinite set of numbers of the second number class was either denumerable ,
or had the cardinal number (a) . The final step was a short one , but he still had to
...
Joseph Warren Dauben,
1990
WIADOMOŚCI, KTÓRE ZAWIERAJĄ SŁOWO «CARDINAL NUMBER»
Sprawdź, o czym dyskutuje się w prasie krajowej i zagranicznej oraz jak jest stosowane słowo
cardinal number w wiadomościach.
Baseball Recap: Louisville 7 Carolina 4
The Cardinal number 9 hitter, short stop Devin Hairston, then grounded out to second base to bring up Whiting who struck out to end the inning. «Tar Heel Blog, Maj 15»
ANSYS' (ANSS) CEO Jim Cashman on Q1 2015 Results - Earnings …
So, the fact is we're going to have a revenue ramp up from that; it just won't count as that to be very cardinal number of numbers in there. «Seeking Alpha, Maj 15»
Brazilian Actor Wagner Moura Joins “O Magnífico Sete” (The …
Hollywood is continuing the trend of coming up with movie titles using the formula: Definite Article + Adjective + Cardinal Number. This year we ... «2paragraphs.com, Kwi 15»
All Hail Sam: SFA's Record Against Their Piney Woods Rival
O-N-E. Definition: “the lowest cardinal number; half of two; 1.” Alright, alright, calm yourselves. Back down Lumberjacks, it's just one sport – and surely its a fluke. «The Sawmill, Mar 15»
How to Count the Defensive Use of Guns
To the people involved in these incidents, no number of DGUs is more important than the cardinal number representing them. Kleck rose to his ... «Reason, Mar 15»
4 Tips for Small Businesses to Decide on a Memorable Brand Name
A few rounds of discussions later at their Stanford University office, they zeroed in on Googol, which is a cardinal number represented as 1 ... «Business 2 Community, Lut 15»
No Man's Sky - The Game We'll Be Showing Our Grandkids!
Let's take a look at what that means: A cardinal number represented in the U.S. by 1 followed by 18 zeros, and in Great Britain by 1 followed by ... «moviepilot.com, Sty 15»
11 words that mean something completely different at The University …
What is means everywhere else: a cardinal number. What it means at the University of Alabama: Number of national college football ... «AL.com, Wrz 14»
5 Annual award for American journalism, literature or music (8,5)
... 14 Brave guy (4); 15 Plan (6); 16 Roman goddess of the dawn (6); 17 French city on the Loire (6); 19 Illumination (5); 20 Cardinal number (5) ... «The Guardian, Maj 14»
China Spectacles Industry Report, 2013-2015
Nevertheless, given the large cardinal number of Chinese population, there are three to four million Chinese people in need for corrective ... «MarketWatch, Lut 14»