Cardinality and Countability Types ..PDF

Cardinality

1. CARDINALITY SALFORD & CO.
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Number of distinct elements in a set is know as cardinality
or cardinal numbers .
Denoted by n(A) or (A)
Examples :
1) A= {a,b,c,d,e,} n(A)= 5
2) B= {a,a,b,d,d} n(B)= 3
3) C= {a,{c,d},k} n(C)= 3
Presented by
Habiba Mirza

2. CARDINALITY OF SET
- Basically it is the number of objects in a set
1) If i have a set of days in a week and it is represented by A
so its Cardinality will be
n(A)= 7
2) If i have a set of even numbers less than 10 and it is
represented by B so its Cardinality will be
n(B)= {0,2,4,8} = 4
3) If i have a set of Cardinality of all even numbers and it is
represented by C then it's Cardinality will be
n(C)= infinity ♾️
4) Cardinality of all sets of prime number less than
100 will be n(A)= 25

3. For the Cardinality of Infinite numbers we use symbols to
denote their Cardinality.
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CARDINALITY OF
INFINITE SET
For Natural numbers
|N|= ℵ0 (aleph null)
For Real numbers
|R|= c ( continum)

4. TYPES OF CARDINALITY
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One to one Cardinality
When one occurrence of an Entity is associated with
exactly one occurrence of another Entity.
Example
If a person and passport are two identities, then one
person can have exactly one passport and only one
passport can be assigned to a person.
A many-to-many relationship is a type of cardinality that refers
to the relationship between two entities, say, A and B, where A
may contain a parent instance for which there are many
children in B and vice versa.
Many to many Cardinality
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Mafia Parveen

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One to many Cardinality
A one-to-many relationship is a type of cardinality that refers to
the relationship between two entities (see also entity–relationship
model) A and B in which an element of A may be
linked to many elements of B, but a member of B is linked to only
one element of A.
Example
For example, one teacher can teach many students at a time. But,
many teachers cannot teach a single student at a time
Example
A student, for example, can be taking zero or more
courses, while a course can have zero or more students.

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Countability
In mathematics, countabritilty is often used to classify sets
based on the size of their elements.
Countabritilty refers to the property of a set that allows
its elements to be counted, either finitely or infinitely
uses
Types
1) Countable Finite
2) Countable Infinite
Presented by
Mahnoor,
Maryam and
Areej

7. COUNTABLE FINITE
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Set is countably finite if it has a finite number of
elements that can be counted.
Consider the set S = {1, 2, 3, 4, 5}. This set is countably
finite because it contains 5 elements that can be
counted.
Exmaple

8. An example of a countably infinite set is the set of all even numbers, E =
{2, 4, 6, 8, ...}.
Although this set continues indefinitely, the elements can still be
counted by pairing them with the natural numbers
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COUNTABLE INFINITE
A set is countably infinite if its elements can be put
into a one-to-one correspondence with the set of
natural numbers (1, 2, 3, 4, ...).
Exmaple