# Sets

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Set theory is about studying collection of objects. The collection may comprise anything or any abstraction. It can be purely abstract thing like numbers or abstraction of real thing like students studying in class XI in a school. The members of collection can be numbers, letters, titles of books, people, teachers, provinces – virtually anything - even other collections. Further, it need not be finite. For example, a set of integers has infinite members. For a set, only requirement is that the members of a collection are properly defined.

Set
A set is a collection of well defined objects.

In other words, the member of set is clearly identifiable. The terms “object”, “member” or “element” mean same thing and are used interchangeably.

## How to represent a set?

A set is denoted by capital letters like “A”, “B”, “C” etc. In choosing a symbol for a set, it is generally convenient to use a capital letter that identifies with the set. For example, it is appropriate to use symbol “V” to represent collection of vowels in English alphabet.

On the other hand, the members or elements of a set are denoted by small letters like “a”,”b”,”c” etc.

Membership of a set is denoted by the symbol “ $\in$ ” . Its literal meaning is “belongs to”. If an object does not belong to a set, then we convey the same, using symbol “ $\notin$ ”.

$a\in A$ : we read this as “a” belongs to set "A".

$a\notin A$ : we read this as “a” does not belong to set "A".

The set is represented in two ways :

• Roaster form
• Set builder form

## Roaster form

All elements of the set are listed with a comma (“,”) in between and the listing itself is enclosed within braces “{“ and “}”. The order or sequence of elements within the set is not important – though desirable.

The set of numbers, which divide 12, is written as :

$A=\left\{1,2,3,4,6,12\right\}$

If a pattern or sequence is easily made out, then we can use ellipsis ("...") to represent continuity of such pattern. This type of representation is particularly useful to represent an infinite set. Clearly, sequence of members in this type of representation is important.

The set of even numbers is written as,

$B=\left\{2,4,6,8\dots \dots \dots \right\}$

The roaster form is limited in certain circumstance. For example, we can not represent set of real numbers in roaster form. Real numbers is an infinite set, but the elements of this set do not follow a pattern or have a particular sequence. As such, we can not define same with the help of ellipsis.

Every member of the set is unique and distinct. However, we encounter situations in which collection can have repeated elements. For example, the set representing scores of three students can be a set of three numbers one of which is repeated :

$S=\left\{80,80,70\right\}$

We need to reduce such collection as :

$⇒S=\left\{80,80,70\right\}=\left\{80,70\right\}$

## Set builder form

Collections are often characterized by a common property. We can, therefore, define members of a set in terms of the common property. However, we need to ensure that objects outside the collection do not have the same common property.

The construction of qualification for the common property is quite flexible. Only thing is that we need to be explicit in what we mean. Generally, we denote the member by a symbol like “x” and then define the membership. Consider the examples :

#### Questions & Answers

Do somebody tell me a best nano engineering book for beginners?
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
what is the Synthesis, properties,and applications of carbon nano chemistry
so some one know about replacing silicon atom with phosphorous in semiconductors device?
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Harper
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
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many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
what is nano technology
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preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
how did you get the value of 2000N.What calculations are needed to arrive at it
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