How to Tackle Recursion

In the previous post we have discussed about How to Define Complements in Mathematics and In today's session we are going to discuss about how to Tackle Recursion. The term recursion is generally used in many subjects including the subject of the math. Many of us do not exactly know the meaning of this term in the context of the math. So in this article we will have a look on some of the important facts of the term recursion. (know more about Radical, here)

Now let us start with the definition of the term recursion. It is a method in which we repeat the items in a way which is self similar. It should be noticed that in a situation where the surfaces of any 2 mirrors are completely parallel to each other then the nested type of the images which we see can be said to be the form of an infinite type of the recursion. This term can give different types of the meanings especially to the varieties of the disciplines which range from the linguistics to the logic.
We will now discuss about some of the uses of the recursion. One of its very common uses in the field of the mathematics is the one where it is being referred to a process in which we define the functions where the function which is defined is being applied within the definition of its own.   
Particularly it can be used to define almost infinite no. of the instances that is the values of the function with the help of an expression which is finite which for some of the instances may be referred to other of the instances but in that way where any loop or a chain which is infinite cannot occur. However the term recursion is also utilized very commonly to explain any process of the objects which are repeating in a way which is self similar.
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How to Define Complements in Mathematics

In the previous post we have discussed about How to Read Binary and In today's session we are going to discuss about Complements, the word Complements can be refered as a concept that perform there different task in various field of mathematics. In a simple mean we can say that complement is a amount which can be added to something of same kind to generate its whole. The definition of Complement varies according to the different fields of mathematics.
In the geometrical mathematics the word Complements can be express as angle of 90 degree which is formed by adding two different angles. In geometry, one angle said to be complement for the other angle to make a whole angle. Suppose the measure of one angle is 35 degree and the measure of other is 55 degree then merge up of these angles form a 90 degree angle that can be consider as a whole angle.
In the same aspect of set theory, the word  Complements can be define as a inverse of any set. As we know that a set is a collection of elements that are also exists in universal set. In the same aspect the concept of complement for a set S can be define as a set of all elements that are not exists in the set A. Suppose there is a set B, so the Complements of B contains all the elements that are exists in universal set U but do not contain by set B. In the mathematical notation complement of set can be express as below given format:
Complement of B = (B)'
Suppose the set B = (1, 2, 3 ) And Universal set U contains (a, b, c, 1, 2, 3) then 
Complements of set B can be represented as in below given format:
B' = (a, b, c)
when we add both set then it make whole set which can be called as universal set. It means to say that set B + Set B' = U set.
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How to Read Binary

In the previous post we have discussed about How Online Matrix Calculator and In today's session we are going to discuss about How to Read Binary. Decimal Numbers are the numbers which include 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 . We do all our mathematical processing in the form of decimal numbers. Binary numbers are the numbers which can be expressed in the form of 1 and 0 only. The data stored in the computers, calculators, chip is all in the form of digits and so it is in the form of binary codes.  These Binary numbers can be converted in the form of decimal numbers. Here we are going to learn about How To Read Binary.
Let us take the example of the binary number say 1 0 0 1. To convert the given binary number, we will start reading the data from the right hand side and place the numbers with base 2 and power 0 at the first place. The power goes on increasing by 1as we move from right to the left. SO the first digit will be 2 >0 = 1, followed by 2 >1 = 2, then we proceed as follows:
2>2 = 2 * 2 = 4
2>3 = 2 * 2 * 2  = 8
2> 4 = 2 * 2* 2 * 2  = 16
Thus the series appears as follows: 1, 2, 4, 8, 16 , 32 . . . .. .. which will be written along with the binary digits starting by right as follows
 8      4        2       1
1       0        0       1
Now we write 1 * 8 +  4 * 0 + 2 * 0 + 1 *1 = 8 + 0 + 0 + 1 = 9, which is the decimal number. (know more about Binary, here)


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How Online Matrix Calculator

In the previous post we have discussed about How to Understand Functions and In today's session we are going to discuss about How Online Matrix Calculator. In this blog we are going to discuss about the on line matrix calculator that is an on line tool for calculation on the given matrix. It is solved the desired operation on the given matrix in very less period of time .For using this tool user only enter the desired matrix into the text box and there are values are separated by the spaces or comma. Calculator calculates all the operations that are specifies in the text box and also give the accurate answer efficiently. There are concepts of calculating the operations on matrix's are different from the general type of operations as addition, subtraction, multiplication or division. (know more about Matrix , here)
There are several operations that are done on the matrix as addition, subtraction, multiplication or division. There are some other operations as inverse of matrix or transposition of matrix are also done by the on line matrix calculator.
 If we have two matrixes a [] and b [] then according to the different operation we can show it as follows:
[ a11 a12 [b11 b12 [ C11 C12
a21 a22 ] <operator> b21 b22] = C21 C22 ]
These matrixes are entered to text box of the on line calculator and select the desired operation that will perform by the calculator and it automatically generates the answer in form of another matrix.
There are also some of the complex calculations that are defined as Matrix Transpose, MatrixInverse done by the online matrix calculator. In some advance online matrix calculator some of the calculations as QR Decomposition and Moore – Pen-rose Inverse and LU Decomposition and Matrix Trace are also performed.
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How to Understand Functions

In the previous post we have discussed about What are Binary Numbers and In today's session we are going to discuss about How to Understand Functions. The concept of functions is of paramount importance in mathematics and among other disciplines as well. Functions are the relation between the set of inputs and the set of possible outputs that a follow a property i. e. each input is associated definitely with one output. (know more about Function, here)
A function 'f' from a set P to a set Q associates each element of set P to a unique element of set Q.
Terms such as “map” (or “mapping”) correspondence used as synonyms for “function”. If f is a function from a set P to a set Q, then we write f: P → Q or P → Q, which is read as f is a function from P to Q or f maps P to Q.
We use some standard real function such as constant, identity, modulus, greatest integer, smallest integer function and many more. We can also perform many operations on the above function like addition, product, subtraction, quotient etc.
There are some types of function are defined in calculus.

I.            One -one function: - It is also known as injection function. If different items of P have different images in Q, then it is said to be one-one function.

II.            Many-one function:- If two or more items of a set P have the same image In Q, then it is said to be many-one function.

III.            Onto function: - It is also known as surjection function. If every element of Q is the F-image of some element of P, then it is said to be onto function.

IV.            One-one onto function: - It is also known as bijection function. If it is one-one as well as onto, then it is said to be one-one onto function.

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What are Binary Numbers

In the previous post we have discussed about binary subtraction and In today's session we are going to discuss about What are Binary Numbers. In mathematics, binary number plays a vital role in the study of number system. What are binary numbers? Many students ask this question. Binary number composed or involved of two number i.e. 0 and 1. There are many operations which are performed by the binary number such as addition, subtraction, multiplication and division. The state of 0 is off and 1 is on.
Binary numbers are basically used in logic gates, computers and many digital electronics circuits.
Let’s deal with the addition of binary number:
Addition of binary number is carried by two steps:

·         1+ 1 = 0 and the carry left goes to the other column.

·         1+ 0 = 1

Suppose we have to add two binary numbers:
Example:
   0 0 0 1 1 1 1 0
+ 1 1 1 0 0 0 1 0
 1 0 0 0 0 0 0 0 0
Here carry 1 goes to the next column.
Now, subtraction of binary number is given by:

·         1 – 0 = 1

·         1 – 1 = 0

·         0 – 0 = 0

·         0 – 1 = 1(with carry from the left side)

Suppose we have to subtract two number:
Example:
   1 1 0 1 (in decimal this is 13)
  -0 1 1 1 (in decimal this is 7)
   0 1 1 0  (so the resultant is 6 in decimal)
( in the first column from the right there is 1-1=0, in the second column 0-1=1 and 1 is carry from the left one, in third column there is 0 remaining in the place of 1 so it will also take carry from left one so the subtraction is 1and in the fourth column 0-0=0 so the total result is 0 1 1 0 ).
Some binary numbers are given below:
The code for binary number is A B C D
                                                8 4 2 1
1 = 0001
2 = 0010
3 =0011
And so on.
Binary numbers and significant figures calculator are well described in CBSE board.

binary subtraction

Now today we will discuss about binary subtraction. In the mathematics the number which has base two is known as binary number. In binary number system only two digits are used which are 0 and 1.
For example: 1011 represents (1 × 2³) + (0 × 2²) + (1 × 2¹) + (1 × 2⁰), they represent 8 + 0 + 2 + 1, and equals to 11.
Now we will see the binary subtraction.
To finding the subtraction in the binary number system we have to follow some of the step which is given below.
Step1: Calculating subtraction first we take the number.
Step2: It is necessary to remember that the number should be in the form of 0 and 1 binary digit.
Step3: Subtracting the values we have to follow such above conditions, if we subtract the number 0 from the number 0 then we get 0. When we subtract number 1 from the number 0 then we get 1. We subtract the number 0 from the number 1 then we get 1 with borrow. When we subtract the number 1 from the number 1 then we get 0, all these values have base 2 because the binary number is defined in the base 2 only.
Suppose we have 01010 and 1010, and we to do subtraction then it can be done as shown below.
For subtraction we need to follow above steps to find the result.
Step1: First take two numbers and the numbers should be in the form of binary number system.
01010 and 1010,
Step2: Then apply all the steps one by one.
(01010)₂ – (1010)₂
01010
  1010
If we subtract 0 from 0 then we get 0; rule number 1;
01010
  1010
        0
If we subtract 1 from 1 then we get 0; apply rule number 4;
01010
  1010
      00
now subtract 0 from 0 we get 1.
01010
  1010
    000
Now we subtract 1 from 1 then we get 0.
01010
  1010
  0000
Now borrow will add to next digit. So the number is:
01010
  1010
 10000
So the value is 10000.
Gamma Distribution is related to the statistical distribution which is also related to the beta distribution. ICSE examination is organised by the council for the Indian school certificate examination and in next session we will discuss about What are Binary Numbers.

one-to-one correspondence

In the previous post we have discussed about truth table and In today's session we are going to discuss about one-to-one correspondence, It is a condition when all the elements of one set say set ‘T’ is matched with the member of other set say set ‘R’ . The other name of the one-to-one correspondence is bijection and bijective function. Here none of the member of the set remains unpaired. It means each element of one set is paired with the other element of the other set. The one-to-one correspondence from set T to set R has the inverted function from set T to set R. also we can say this if set T and set R has the finite number of elements then the presence of one-to-one correspondence states that the sets pursue the same number of element. One-to-one correspondence from all the sets to all members of the set are sometime termed as permutation. One-to-one correspondence also has many applications in many areas of mathematics which include definitions of permutation group, projective map, homeomorphism, etc.
To do the perfect pairing with between the set T and set R one-to-one correspondence must follow four properties, they are:

•  Each element of the set ‘T’ must be paired with one of the element of set ‘R’.
• Not even a single member of set ‘T’ should be repeated to form the pair with other member of set ‘R’.
• Each element of set ‘R’ must be matched with at least one element of set ‘T’.
  • None of the member of set ‘R’ can be paired with the more than one element of set ‘

If the one to one correspondence satisfies the first two properties than it is surjective in nature and if it satisfies the last two properties than it is injective in nature, Hence we can conclude this the one-to-one correspondence is both surjective and injective in nature.

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truth table

A truth table is a table in mathematics used in logic especially in representation in Boolean algebra, it is also an alternate of truth table, It is used for the calculation of functional values on each expressions on their arguments. It simple words we can say that this table help us in checking whether an expression result is true for all the values we enter as input or it is logically valid
Representation of a truth table is where one column is for the input variable individually and one column for all the results of the operation for which this table is designed. The top row represents the variables from the expressions and various combinations
It is breaking of logic functions by identifying all the values the expression can have. It normally represents two input columns but can be increased up to any number according to the requirement of the problem. The values in input column are in the form of binary numbers
The three operations basic functions have are:
1. Not operation-It is also called as negation or inversion and is represented with symbol “-“
2. OR operation-It is called as addition or disjunction operation and is represented with symbol “+”
3. AND operation- It is called as multiplication or conjunction operation and is represented with symbol “*”
These functions are usually assigned the logic values 1 or 0 where 1 means true and 0 means false
Some Rules of the Truth Table are
If X = 0, then -X = 1
If X = 1, then -X = 0
X+Y = 1 except when X = 0 and Y = 0
X+Y = 0 if X = 0 and Y = 0
X*Y = 0 except when X = 1 and Y = 1
X*Y = 1 if X = 1 and Y = 1
For Diameter of a Circle and CBSE board sample papers for class 10 visit online educational portals and In the next session we will discuss about one-to-one correspondence.