Thursday, 18 June 2020

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Thursday, 14 May 2020

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Sunday, 26 April 2020

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Wednesday, 1 August 2018

OOPS : Abstraction, Encapsulation, Inheritance, Polymorphism (OOPS Features)

OOPS : Abstraction, Encapsulation, Inheritance, Polymorphism


OOPS Features

* The object oriented programming (OOP) is a programming model

where Programs are organized around object and data rather than

action and logic.


* OOP allow decomposition of a problem into a number of entities called

Object and then builds data and function around these objects.

The Program is divided into number of small units called Object. The data and function are build around these objects.
The data of the objects can be accessed only by the functions associated with that object.
The functions of one object can access the functions of other object.

OOP has the following important features.

 Class:
A class is the core of any modern Object Oriented Programming language such as C#.
In OOP languages it is must to create a class for representing data.
Class is a blueprint of an object that contains variables for storing data and functions to performing operations on these data.
Class will not occupy any memory space and hence it is only logical

representation of data.
To create a class, you simply use the keyword "class" followed by the class name:
class Employee
{

}
Object: 

Objects are the basic run-time entities in an object oriented system.They may represent a person,a place or any item that the program has to handle.

"Object is a Software bundle of related variable and methods. "

“Object is an instance of a class”




Class will not occupy any memory space. Hence to work with the data represented by the class you must create a variable for the class, which is called as an object.
When an object is created by using the keyword new, then memory will be allocated for the class in heap memory area, which is called as an instance and its starting address will be stored in the object in stack memory area.
 When an object is created without the keyword new, then memory will not be allocated in heap I.e. instance will not be created and object in the stack contains the value null.
When an object contains null, then it is not possible to access the members of the class using that object.

class Employee
{

}
Syntax to create an object of class Employee:-

Employee objEmp = new Employee();


All the programming languages supporting object oriented Programming will be supporting these three main concepts:
Encapsulation
Inheritance
Polymorphism

Abstraction:
Abstraction is "To represent the essential feature without representing the back ground details."

Abstraction lets you focus on what the object does instead of how it does it.

Abstraction provides you a generalized view of your classes or object by providing relevant information.

Abstraction is the process of hiding the working style of an object, and showing the information of an object in understandable manner.

Real world Example of Abstraction: - 
Suppose you have an object Mobile Phone.

Suppose you have 3 mobile phones as following:-

Nokia 1400 (Features:- Calling, SMS)
Nokia 2700 (Features:- Calling, SMS, FM Radio, MP3, Camera)
Black Berry (Features:-Calling, SMS, FM Radio, MP3, Camera, Video Recording, Reading E-mails)

Abstract information (Necessary and Common Information) for the object "Mobile Phone" is make a call to any number and can send SMS."

so that, for mobile phone object you will have abstract class like following:-

    abstract class MobilePhone
    {
        public void Calling();
        public void SendSMS();
    }

    public class Nokia1400 : MobilePhone
    {

    }

    public class Nokia2700 : MobilePhone
    {
        public void FMRadio();
        public void MP3();
        public void Camera();
    }

    public class BlackBerry : MobilePhone
    {
        public void FMRadio();
        public void MP3();
        public void Camera();
        public void Recording();
        public void ReadAndSendEmails();

    }

Abstraction means putting all the variables and methods in a class which are necessary.
For example: - Abstract class and abstract method.
Abstraction is the common thing.
example:
If somebody in your collage tell you to fill application form, you will fill your details like name, address, data of birth, which semester, percentage you have got etc.
If some doctor gives you an application to fill the details, you will fill the details like name, address, date of birth, blood group, height and weight.
See in the above example what is the common thing?
Age, name, address so you can create the class which consist of common thing that is called abstract class.
That class is not complete and it can inherit by other class.

Encapsulation:
Wrapping up data member and method together into a single unit (i.e. Class) is called Encapsulation.

Encapsulation is like enclosing in a capsule. That is enclosing the related operations and data related to an object into that object.

Encapsulation is like your bag in which you can keep your pen, book etc. It means this is the property of encapsulating members and functions.

    class Bag
    {
        book;
        pen;
        ReadBook();
    }


Encapsulation means hiding the internal details of an object, i.e. how an object does something.

Encapsulation prevents clients from seeing its inside view, where the behaviour of the abstraction is implemented.

Encapsulation is a technique used to protect the information in an object from the other object.

Hide the data for security such as making the variables as private, and expose the property to access the private data which would be public.
So, when you access the property you can validate the data and set it.

Example:

class Demo
{
   private int _mark;

   public int Mark
   {
     get { return _mark; }
     set { if (_mark > 0) _mark = value; else _mark = 0; }
   }
 }

Real world Example of Encapsulation:-
Let's take example of Mobile Phone and Mobile Phone Manufacturer
Suppose you are a Mobile Phone Manufacturer and you designed and developed a Mobile Phone design(class), now by using machinery you are manufacturing a Mobile Phone(object) for selling, when you sell your Mobile Phone the user only learn how to use the Mobile Phone but not that how this Mobile Phone works.

This means that you are creating the class with function and by making object (capsule) of it you are making availability of the functionality of you class by that object and without the interference in the original class.

Example-2:
TV operation
It is encapsulated with cover and we can operate with remote and no need to open TV and change the channel.
Here everything is in private except remote so that anyone can access not to operate and change the things in TV.


Inheritance: 
When a class acquire the property of another class is known as inheritance.
Inheritance is process of object reusability.
For example, A Child acquire property of Parents.

public class ParentClass
    {
        public ParentClass()
        {
            Console.WriteLine("Parent Constructor.");
        }

        public void print()
        {
            Console.WriteLine("I'm a Parent Class.");
        }
    }

    public class ChildClass : ParentClass
    {
        public ChildClass()
        {
            Console.WriteLine("Child Constructor.");
        }

        public static void Main()
        {
            ChildClass child = new ChildClass();

            child.print();
        }
    }



Output:
    Parent Constructor.
    Child Constructor.
    I'm a Parent Class.

Polymorphism: 


Polymorphism means one name many forms.
One function behaves different forms.
In other words, "Many forms of a single object is called Polymorphism."

Real World Example of Polymorphism:
Example-1:
A Teacher behaves to student.
A Teacher behaves to his/her seniors.
Here teacher is an object but attitude is different in different situation.
Example-2:
Person behaves SON in house at the same time that person behaves EMPLOYEE in office.
Example-3:
Your mobile phone, one name but many forms
As phone
As camera
As mp3 player
As radio
To Read Polmorphism in Detail click following link:-

Polymorphism in .Net



Difference between Abstraction andEncapsulation :-

Abstraction
Encapsulation
1. Abstraction solves the problem in the design level.

1. Encapsulation solves the problem in the implementation level.

2. Abstraction is used for hiding the unwanted data and giving relevant data.

2. Encapsulation means hiding the code and data into a single unit to protect the data from outside world.


3. Abstraction lets you focus on what the object does instead of how it does it

3. Encapsulation means hiding the internal details or mechanics of how an object does something.

4. Abstraction- Outer layout, used in terms of design.
For Example:-
 Outer Look of a Mobile Phone, like it has a display screen and keypad buttons to dial a number.

4. Encapsulation- Inner layout, used in terms of implementation.
For Example:- Inner Implementation detail of a Mobile Phone, how keypad button and Display Screen are connect with each other using circuits.

For Example:-
 Outer Look of a Mobile Phone, like it has a display screen and keypad buttons to dial a number.

4. Encapsulation- Inner layout, used in terms of implementation.
For Example:- Inner Implementation detail of a Mobile Phone, how keypad button and Display Screen are connect with each other using circuits.


The easier way to understand Abstraction and encapsulation is as follows:-
Real World Example:-

Take an example of Mobile Phone:-
You have a Mobile Phone, you can dial a number using keypad buttons. Even you don't know how these are working internally. This is called Abstraction. You have the only information that is needed to dial a number. But not its internal working of mobile.

But how the Mobile Phone internally working?, how keypad buttons are connected with internal circuit? is called Encapsulation.

Summary:
"Encapsulation is accomplished by using Class. - Keeping data and methods that accesses that data into a single unit"
"Abstraction is accomplished by using Interface. - Just giving the abstract information about what it can do without specifying the back ground details"
"Information/Data hiding is accomplished by using Modifiers - By keeping the instance variables private or protected."


Constructor types with example programs in C#.NET


Definition:
In simple terms, Constructor is a special kind of method with class name as method name and gets executed when its (class) object is created.
This article will give you a detailed explanation on C# constructors and its types.
Now, when we look at the above definition in a broader sense, a constructor is a class method that gets automatically executed whenever class’s object is created.


A special method of the class that will be automatically invoked when an instance of the class is created is called as constructor.

Constructors can be classified into 5 types
Default Constructor
Parameterized Constructor
Copy Constructor
Static Constructor
Private Constructor
Default Constructor : A constructor without any parameters is called as default constructor. Drawback of default constructor is every instance of the class will be initialized to same values and it is not possible to initialize each instance of the class to different values.

Example for Default Constructor

Parameterized Constructor : A constructor with at least one parameter is called as parameterized constructor. Advantage of parameterized constructor is you can initialize each instance of the class to different values.


Example for Parameterized Constructor

using System;

namespace ProgramCall
{
    class Test1
    {
        //Private fields of class
        int A, B;

        //default Constructor
        public Test1()
        {
            A = 10;
            B = 20;
        }

        //Paremetrized Constructor
        public Test1(int X, int Y)
        {
            A = X;
            B = Y;
        }

        //Method to print
        public void Print()
        {
            Console.WriteLine("A  =  {0}\tB  =  {1}", A, B);
        }     
             
    }

    class MainClass
    {
        static void Main()
        {

            Test1 T1 = new Test1();  //Default Constructor is called
            Test1 T2 = new Test1(80, 40); //Parameterized      Constructor is called       
            T1.Print();
            T2.Print();
            Console.Read();     
        }
    }

}

Output

A  =  10        B  =  20
A  =  80        B  =  40

Copy Constructor : A parameterized constructor that contains a parameter of same class type is called as copy constructor. Main purpose of copy constructor is to initialize new instance to the values of an existing instance.

Example for Copy Constructor
using System;

namespace ProgramCall
{
    class Test2
    {
        int A, B;
        public Test2(int X, int Y)
        {
            A = X;
            B = Y;
        }

        //Copy Constructor
        public Test2(Test2 T)
        {
            A = T.A;
            B = T.B;
        }


   
        public void Print()
        {
            Console.WriteLine("A  =  {0}\tB  =  {1}", A, B);
        } 

    }

    class CopyConstructor
    {
        static void Main()
        {       

            Test2 T2 = new Test2(80, 90);
            //Invoking copy constructor
            Test2 T3 = new Test2(T2);         
            T2.Print();
            T3.Print();
            Console.Read();
        }
    }
}

Output

A  =  80        B  =  90
A  =  80        B  =  90

Static Constructor : You can create a constructor as static and when a constructor is created as static, it will be invoked only once for any number of instances of the class and it is during the creation of first instance of the class or the first reference to a static member in the class. Static constructor is used to initialize static fields of the class and to write the code that needs to be executed only once.

Example for Static Constructor
using System;

namespace ProgramCall
{
    class Test3
    {

        public Test3()
        {

            Console.WriteLine("Instance  Constructor");
        }

        static Test3()
        {
            Console.WriteLine("Static  Constructor");
        }
    }
    class StaticConstructor
    {
        static void Main()
        {
            //Static Constructor and instance constructor, both are invoked for first instance.
            Test3 T1 = new Test3();
            //Only instance constructor is invoked.
            Test3 T2 = new Test3(); 

            Console.Read();
        }
    }
}

Output

Static  Constructor
Instance  Constructor
Instance  Constructor


Private Constructor : You can also create a constructor as private. When a class contains at least one private constructor, then it is not possible to create an instance for the class. Private constructor is used to restrict the class from being instantiated when it contains every member as static.

Some unique points related to constructors are as follows
A class can have any number of constructors.
A constructor doesn’t have any return type even void.
A static constructor can not be a parameterized constructor.
Within a class you can create only one static constructor.
Note
Ø       A static constructor should not be declared with any access modifier.
Ø       A static constructor does not accept parameters
Ø       A static constructor is called automatically.
Ø       There is no way to call a static constructor directly.
Ø       Can’t stop the execution of Static constructor

Points to Remember
Ø       Constructor is nothing but a special method, which initializes the class or its task to initialize the object of it class.
Ø       Its name must be same as the name of class
Ø       This is a special method as constructors do not have return types, not even void
Ø       Constructor cannot return any value because they didn’t have any return type.
Ø       Constructor can’t be get inherited, although a derived class can class the base class constructor.
Ø       A class has atleast one constructor also known as default constructor [a constructor without parameter]
Ø       You have to explicitly write a default constructor while overloading constructors.
Ø       Concept declaring multiple constructors of a class with different sets of parameters known as Constructor overloading.
Ø       A constructor can be called another constructor using this()

Friday, 8 June 2018

Mathematical Symbols and signs - meanings

Mathematical Symbols

List of all mathematical symbols and signs - meaning and examples.
  • Basic math symbols
  • Geometry symbols
  • Algebra symbols
  • Probability & statistics symbols
  • Set theory symbols
  • Logic symbols
  • Calculus & analysis symbols
  • Number symbols
  • Greek symbols
  • Roman numerals

Basic math symbols

SymbolSymbol NameMeaning / definitionExample
=equals signequality5 = 2+3
5 is equal to 2+3
not equal signinequality5 ≠ 4
5 is not equal to 4
approximately equalapproximationsin(0.01) ≈ 0.01,
x ≈ y means x is approximately equal to y
>strict inequalitygreater than5 > 4
5 is greater than 4
<strict inequalityless than4 < 5
4 is less than 5
inequalitygreater than or equal to5 ≥ 4,
x ≥ y means x is greater than or equal to y
inequalityless than or equal to4 ≤ 5,
x ≤ y means x is less than or equal to y
( )parenthesescalculate expression inside first2 × (3+5) = 16
[ ]bracketscalculate expression inside first[(1+2)×(1+5)] = 18
+plus signaddition1 + 1 = 2
minus signsubtraction2 − 1 = 1
±plus - minusboth plus and minus operations3 ± 5 = 8 and -2
±minus - plusboth minus and plus operations3 ∓ 5 = -2 and 8
*asteriskmultiplication2 * 3 = 6
×times signmultiplication2 × 3 = 6
multiplication dotmultiplication2 ⋅ 3 = 6
÷division sign / obelusdivision6 ÷ 2 = 3
/division slashdivision6 / 2 = 3
horizontal linedivision / fraction\frac{6}{2}=3
modmoduloremainder calculation7 mod 2 = 1
.perioddecimal point, decimal separator2.56 = 2+56/100
abpowerexponent23 = 8
a^bcaretexponent2 ^ 3 = 8
asquare root
a ⋅  = a
9 = ±3
3acube root3a ⋅ 3 ⋅ 3 = a38 = 2
4afourth root4a ⋅ 4 ⋅ 4 ⋅ 4a = a416 = ±2
nan-th root (radical) for n=3, n8 = 2
%percent1% = 1/10010% × 30 = 3
per-mille1‰ = 1/1000 = 0.1%10‰ × 30 = 0.3
ppmper-million1ppm = 1/100000010ppm × 30 = 0.0003
ppbper-billion1ppb = 1/100000000010ppb × 30 = 3×10-7
pptper-trillion1ppt = 10-1210ppt × 30 = 3×10-10

Geometry symbols

SymbolSymbol NameMeaning / definitionExample
angleformed by two rays∠ABC = 30°
measured angle ABC = 30°
spherical angle AOB = 30°
right angle= 90°α = 90°
°degree1 turn = 360°α = 60°
degdegree1 turn = 360degα = 60deg
primearcminute, 1° = 60′α = 60°59′
double primearcsecond, 1′ = 60″α = 60°59′59″
lineinfinite line 
ABline segmentline from point A to point B 
rayline that start from point A 
arcarc from point A to point B = 60°
perpendicularperpendicular lines (90° angle)AC ⊥ BC
| |parallelparallel linesAB | | CD
congruent toequivalence of geometric shapes and size∆ABC≅ ∆XYZ
~similaritysame shapes, not same size∆ABC~ ∆XYZ
Δtriangletriangle shapeΔABC≅ ΔBCD
|x-y|distancedistance between points x and yx-y | = 5
πpi constantπ = 3.141592654...
is the ratio between the circumference and diameter of a circle
c = πd = 2⋅πr
radradiansradians angle unit360° = 2π rad
cradiansradians angle unit360° = 2π c
gradgradians / gonsgrads angle unit360° = 400 grad
ggradians / gonsgrads angle unit360° = 400 g

Algebra symbols

SymbolSymbol NameMeaning / definitionExample
xx variableunknown value to findwhen 2x = 4, then x = 2
equivalenceidentical to 
equal by definitionequal by definition 
:=equal by definitionequal by definition 
~approximately equalweak approximation11 ~ 10
approximately equalapproximationsin(0.01) ≈ 0.01
proportional toproportional to
y ∝ x when y = kx, kconstant
lemniscateinfinity symbol 
much less thanmuch less than1 ≪ 1000000
much greater thanmuch greater than1000000 ≫ 1
( )parenthesescalculate expression inside first2 * (3+5) = 16
[ ]bracketscalculate expression inside first[(1+2)*(1+5)] = 18
{ }bracesset 
xfloor bracketsrounds number to lower integer⌊4.3⌋ = 4
xceiling bracketsrounds number to upper integer⌈4.3⌉ = 5
x!exclamation markfactorial4! = 1*2*3*4 = 24
x |single vertical barabsolute value| -5 | = 5
(x)function of xmaps values of x to f(x)(x) = 3x+5
(f ∘ g)function composition(f ∘ g) (x) = (g(x))(x)=3x,g(x)=x-1 ⇒(f ∘ g)(x)=3(x-1)
(a,b)open interval(a,b) = {x | a < x < b}x∈ (2,6)
[a,b]closed interval[a,b] = {x | a ≤ x ≤ b}x ∈ [2,6]
deltachange / differencet = t- t0
discriminantΔ = b2 - 4ac 
sigmasummation - sum of all values in range of series xi= x1+x2+...+xn
∑∑sigmadouble summation
capital piproduct - product of all values in range of series xi=x1∙x2∙...∙xn
ee constant / Euler's numbere = 2.718281828...e = lim (1+1/x)x , x→∞
γEuler-Mascheroni constantγ = 0.5772156649... 
φgolden ratiogolden ratio constant 
πpi constantπ = 3.141592654...
is the ratio between the circumference and diameter of a circle
c = πd = 2⋅πr

Linear Algebra Symbols

SymbolSymbol NameMeaning / definitionExample
·dotscalar product· b
×crossvector product× b
ABtensor producttensor product of A and BA ⊗ B
\langle x,y \rangleinner product  
[ ]bracketsmatrix of numbers 
( )parenthesesmatrix of numbers 
A |determinantdeterminant of matrix A 
det(A)determinantdeterminant of matrix A 
|| x ||double vertical barsnorm 
ATtransposematrix transpose(AT)ij = (A)ji
AHermitian matrixmatrix conjugate transpose(A)ij = (A)ji
A*Hermitian matrixmatrix conjugate transpose(A*)ij = (A)ji
A -1inverse matrixA A-1 = I 
rank(A)matrix rankrank of matrix Arank(A) = 3
dim(U)dimensiondimension of matrix Adim(U) = 3

Probability and statistics symbols

SymbolSymbol NameMeaning / definitionExample
P(A)probability functionprobability of event AP(A) = 0.5
P(A ∩ B)probability of events intersectionprobability that of events A and BP(AB) = 0.5
P(A ∪ B)probability of events unionprobability that of events A or BP(AB) = 0.5
P(A | B)conditional probability functionprobability of event A given event B occuredP(A | B) = 0.3
(x)probability density function (pdf)P( x  b) = ∫ f (x) dx 
F(x)cumulative distribution function (cdf)F(x) = P(X x) 
μpopulation meanmean of population valuesμ = 10
E(X)expectation valueexpected value of random variable XE(X) = 10
E(X | Y)conditional expectationexpected value of random variable X given YE(X | Y=2) = 5
var(X)variancevariance of random variable Xvar(X) = 4
σ2variancevariance of population valuesσ= 4
std(X)standard deviationstandard deviation of random variable Xstd(X) = 2
σXstandard deviationstandard deviation value of random variable XσX  = 2
medianmiddle value of random variable x
cov(X,Y)covariancecovariance of random variables X and Ycov(X,Y) = 4
corr(X,Y)correlationcorrelation of random variables X and Ycorr(X,Y) = 0.6
ρX,Ycorrelationcorrelation of random variables X and YρX,Y = 0.6
summationsummation - sum of all values in range of series
∑∑double summationdouble summation
Momodevalue that occurs most frequently in population 
MRmid-rangeMR = (xmax+xmin)/2 
Mdsample medianhalf the population is below this value 
Q1lower / first quartile25% of population are below this value 
Q2median / second quartile50% of population are below this value = median of samples 
Q3upper / third quartile75% of population are below this value 
xsample meanaverage / arithmetic meanx = (2+5+9) / 3 = 5.333
s 2sample variancepopulation samples variance estimators 2 = 4
ssample standard deviationpopulation samples standard deviation estimators = 2
zxstandard scorezx = (x-x) / sx 
~distribution of Xdistribution of random variable X~ N(0,3)
N(μ,σ2)normal distributiongaussian distribution~ N(0,3)
U(a,b)uniform distributionequal probability in range a,b ~ U(0,3)
exp(λ)exponential distribution(x) = λe-λx , x≥0 
gamma(c, λ)gamma distribution(x) = λ c xc-1e-λx / Γ(c), x≥0 
χ 2(k)chi-square distribution(x) = xk/2-1e-x/2 / ( 2k/2 Γ(k/2) ) 
(k1, k2)F distribution  
Bin(n,p)binomial distribution(k) = nCk pk(1-p)n-k 
Poisson(λ)Poisson distribution(k) = λke-λ / k! 
Geom(p)geometric distribution(k) =  p(1-p) k 
HG(N,K,n)hyper-geometric distribution  
Bern(p)Bernoulli distribution  

Combinatorics Symbols

SymbolSymbol NameMeaning / definitionExample
n!factorialn! = 1⋅2⋅3⋅...⋅n5! = 1⋅2⋅3⋅4⋅5 = 120
nPkpermutation_{n}P_{k}=\frac{n!}{(n-k)!}5P3 = 5! / (5-3)! = 60
nCk

combination_{n}C_{k}=\binom{n}{k}=\frac{n!}{k!(n-k)!}5C3 = 5!/[3!(5-3)!]=10

Set theory symbols

SymbolSymbol NameMeaning / definitionExample
{ }seta collection of elementsA = {3,7,9,14},
B = {9,14,28}
A ∩ Bintersectionobjects that belong to set A and set BA ∩ B = {9,14}
A ∪ Bunionobjects that belong to set A or set BA ∪ B = {3,7,9,14,28}
A ⊆ BsubsetA is a subset of B. set A is included in set B.{9,14,28} ⊆ {9,14,28}
A ⊂ Bproper subset / strict subsetA is a subset of B, but A is not equal to B.{9,14} ⊂ {9,14,28}
A ⊄ Bnot subsetset A is not a subset of set B{9,66} ⊄ {9,14,28}
A ⊇ BsupersetA is a superset of B. set A includes set B{9,14,28} ⊇ {9,14,28}
A ⊃ Bproper superset / strict supersetA is a superset of B, but B is not equal to A.{9,14,28} ⊃ {9,14}
A ⊅ Bnot supersetset A is not a superset of set B{9,14,28} ⊅ {9,66}
2Apower setall subsets of A 
\mathcal{P}(A)power setall subsets of A 
A = Bequalityboth sets have the same membersA={3,9,14},
B={3,9,14},
A=B
Accomplementall the objects that do not belong to set A 
A \ Brelative complementobjects that belong to A and not to BA = {3,9,14},
B = {1,2,3},
A-B = {9,14}
A - Brelative complementobjects that belong to A and not to BA = {3,9,14},
B = {1,2,3},
A-B = {9,14}
A ∆ Bsymmetric differenceobjects that belong to A or B but not to their intersectionA = {3,9,14},
B = {1,2,3},
A ∆ B = {1,2,9,14}
A ⊖ Bsymmetric differenceobjects that belong to A or B but not to their intersectionA = {3,9,14},
B = {1,2,3},
A ⊖ B = {1,2,9,14}
a∈Aelement ofset membership A={3,9,14}, 3 ∈ A
x∉Anot element ofno set membershipA={3,9,14}, 1 ∉ A
(a,b)ordered paircollection of 2 elements 
A×Bcartesian productset of all ordered pairs from A and B 
|A|cardinalitythe number of elements of set AA={3,9,14}, |A|=3
#Acardinalitythe number of elements of set AA={3,9,14}, #A=3
aleph-nullinfinite cardinality of natural numbers set 
aleph-onecardinality of countable ordinal numbers set 
Øempty setØ = { }C = {Ø}
\mathbb{U}universal setset of all possible values 
\mathbb{N}0natural numbers / whole numbers  set (with zero)\mathbb{N}0 = {0,1,2,3,4,...}0 ∈ \mathbb{N}0
\mathbb{N}1natural numbers / whole numbers  set (without zero)\mathbb{N}1 = {1,2,3,4,5,...}6 ∈ \mathbb{N}1
\mathbb{Z}integer numbers set\mathbb{Z} = {...-3,-2,-1,0,1,2,3,...}-6 ∈ \mathbb{Z}
\mathbb{Q}rational numbers set\mathbb{Q} = {| x=a/ba,b\mathbb{Z}}2/6 ∈ \mathbb{Q}
\mathbb{R}real numbers set\mathbb{R} = {x | -∞ < x <∞}6.343434∈\mathbb{R}
\mathbb{C}complex numbers set\mathbb{C} = {| z=a+bi, -∞<a<∞,      -∞<b<∞}6+2i ∈ \mathbb{C}

Logic symbols

SymbolSymbol NameMeaning / definitionExample
andandx  y
^caret / circumflexandx ^ y
&ampersandandx & y
+plusorx + y
reversed caretorx ∨ y
|vertical lineorx | y
x'single quotenot - negationx'
xbarnot - negationx
¬notnot - negation¬ x
!exclamation marknot - negationx
circled plus / oplusexclusive or - xorx ⊕ y
~tildenegationx
implies  
equivalentif and only if (iff) 
equivalentif and only if (iff) 
for all  
there exists  
there does not exists  
therefore  
because / since  

Calculus & analysis symbols

SymbolSymbol NameMeaning / definitionExample
\lim_{x\to x0}f(x)limitlimit value of a function 
εepsilonrepresents a very small number, near zeroε  0
ee constant / Euler's numbere = 2.718281828...e = lim (1+1/x)xx→∞
y 'derivativederivative - Lagrange's notation(3x3)' = 9x2
y ''second derivativederivative of derivative(3x3)'' = 18x
y(n)nth derivativen times derivation(3x3)(3) = 18
\frac{dy}{dx}derivativederivative - Leibniz's notationd(3x3)/dx = 9x2
\frac{d^2y}{dx^2}second derivativederivative of derivatived2(3x3)/dx2 = 18x
\frac{d^ny}{dx^n}nth derivativen times derivation 
\dot{y}time derivativederivative by time - Newton's notation 
time second derivativederivative of derivative 
Dyderivativederivative - Euler's notation 
Dx2ysecond derivativederivative of derivative 
\frac{\partial f(x,y)}{\partial x}partial derivative ∂(x2+y2)/∂x = 2x
integralopposite to derivation∫ f(x)dx
∫∫double integralintegration of function of 2 variables∫∫ f(x,y)dxdy
∫∫∫triple integralintegration of function of 3 variables∫∫∫ f(x,y,z)dxdydz
closed contour / line integral  
closed surface integral  
closed volume integral  
[a,b]closed interval[a,b] = {| a  x  b} 
(a,b)open interval(a,b) = {| a < x < b} 
iimaginary uniti ≡ √-1z = 3 + 2i
z*complex conjugate= a+bi → z*=a-biz* = 3 - 2i
zcomplex conjugate= a+bi → = a-biz = 3 - 2i
nabla / delgradient / divergence operatorf (x,y,z)
vector  
unit vector  
* yconvolutiony(t) = x(t) * h(t) 
Laplace transformF(s) = {(t)} 
Fourier transformX(ω) = {(t)} 
δdelta function  
lemniscateinfinity symbol 

Numeral symbols

NameEuropeanRomanHindu ArabicHebrew
zero0 ٠ 
one1I١א
two2II٢ב
three3III٣ג
four4IV٤ד
five5V٥ה
six6VI٦ו
seven7VII٧ז
eight8VIII٨ח
nine9IX٩ט
ten10X١٠י
eleven11XI١١יא
twelve12XII١٢יב
thirteen13XIII١٣יג
fourteen14XIV١٤יד
fifteen15XV١٥טו
sixteen16XVI١٦טז
seventeen17XVII١٧יז
eighteen18XVIII١٨יח
nineteen19XIX١٩יט
twenty20XX٢٠כ
thirty30XXX٣٠ל
forty40XL٤٠מ
fifty50L٥٠נ
sixty60LX٦٠ס
seventy70LXX٧٠ע
eighty80LXXX٨٠פ
ninety90XC٩٠צ
one hundred100C١٠٠ק

Greek alphabet letters

Upper Case LetterLower Case LetterGreek Letter NameEnglish EquivalentLetter Name Pronounce
ΑαAlphaaal-fa
ΒβBetabbe-ta
ΓγGammagga-ma
ΔδDeltaddel-ta
ΕεEpsiloneep-si-lon
ΖζZetazze-ta
ΗηEtaheh-ta
ΘθThetathte-ta
ΙιIotaiio-ta
ΚκKappakka-pa
ΛλLambdallam-da
ΜμMumm-yoo
ΝνNunnoo
ΞξXixx-ee
ΟοOmicronoo-mee-c-ron
ΠπPippa-yee
ΡρRhorrow
ΣσSigmassig-ma
ΤτTautta-oo
ΥυUpsilonuoo-psi-lon
ΦφPhiphf-ee
ΧχChichkh-ee
ΨψPsipsp-see
ΩωOmegaoo-me-ga

Roman numerals

NumberRoman numeral
0not defined
1I
2II
3III
4IV
5V
6VI
7VII
8VIII
9IX
10X
11XI
12XII
13XIII
14XIV
15XV
16XVI
17XVII
18XVIII
19XIX
20XX
30XXX
40XL
50L
60LX
70LXX
80LXXX
90XC
100C
200CC
300CCC
400CD
500D
600DC
700DCC
800DCCC
900CM
1000M
5000V
10000X
50000L
100000C
500000D
1000000M


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