one-to-one function one-to-one function or injective function is one of the most common functions used. One-to-One functions define that each element of one set say Set (A) is mapped with a unique element of another set, say, Set (B). To understand this, let us consider ‘f’ is a function whose domain is set A. The … Read more
If we combine two functions in such a way that the output of one function becomes the input to another function, then this is called as composite function. Consider three sets X, Y and Z and let f: X → Y and g: Y → Z. As per this, under f, an element x∈ X is mapped to … Read more
Let f: X → Y. Now, let f represent a one to one function and y be any element of Y, there exists a unique element x ∈ X such that y = f(x).Then the map f−1: f[X] →X That associates to each element is called as the inverse map of f. The function f(x) = x5 and g(x) = x1/2 have the following property: f(g(x)) = f(x1/5) = (x1/5)5 = x g(f(x)) = g(x5) = (x5)1/5 = x … Read more
*, a binary operation on a set A is basically a function *: A × A → A. We denote * (a, b) by a * b. if a * b = b * a for every a, b ∈ X, a binary operation * on the set X is called commutative. A binary operation … Read more
A symmetric relation is nothing but a type of a binary relation. The relation “is equal to”, is symmetric because if a = b is true then b = a is also true. In formal terms, a binary relation Rover a set X is symmetric only in the following condition: If RT represents the converse of R, then R is symmetric if and only if R = RT Let A be a set and R be the relation … Read more
A relation which is reflexive, symmetric and transitive is an Equivalence relation on set.Relation R, defined in a set A, is said to be an equivalence relation only on the following conditions: (i) aRa for all a ∈ A, that is,R is reflexive. (ii) aRb⇒bRa for all a, b ∈ AR, that is, is symmetric … Read more
In maths, any relation R over a set X is called reflexive if every element of X is related to itself. In formal terms, this may be written as ∀x ∈ X : x R x. The relation “is equal to” on the set of real numbers is an example of a reflexive, since every real number is equal to itself. A reflexive relation is said to possess reflexivity … Read more
Referred to as the sequence of number in a considerable order, you may observe that we very often come across arithmetic problems in regular lives. These considerable patterns of sequences and series have been addressed as progressions in mathematics. Definition of Arithmetic Progression A progression could generally be expressed as a special sequence for which … Read more
Mathematics covers arithmetic series and sequences as a few among the basic topics. While a sequence could be expressed as a collection of elements which allows repetition of any sorts; a series is a sum of all the elements. Solving problems and understanding its fundamentals is likely to make the concept clearer. These are however … Read more
Simple applications (Permutations and Combinations) Counting is considered to be one of the foundation stones in mathematics and the most basic things that you would get to learn. The use of permutations and combinations while dealing with larger data would be of great help. Even of not in its purest and the most accurate forms, … Read more