Mapping onto vs one to one series#

It is a function which assigns to b, a unique element a such that f(a) = b. The inverse of bijection f is denoted as f -1.

Inverse Functions:Bijection function are also known as invertible function because they have inverse function property.

One to one correspondence function(Bijective/Invertible): A function is Bijective function if it is both one to one and onto function.

It is not required that a is unique The function f may map one or more elements of A to the same element of B.

Onto Function (surjective): If every element b in B has a corresponding element a in A such that f(a) = b.

We can express that f is one-to-one using quantifiers as or equivalently, where the universe of discourse is the domain of the function.

It never maps distinct elements of its domain to the same element of its co-domain.

One to one function(Injective): A function is called one to one if for all elements a and b in A, if f(a) = f(b),then it must be the case that a = b.

Equality: Two functions are equal only when they have same domain, same co-domain and same mapping elements from domain to co-domain.

Addition and multiplication: let f1 and f2 are two functions from A to B, then f1 + f2 and f1.f2 are defined as-:.

Image and Pre-Image РІР‚вЂњ b is the image of a and a is the pre-image of b if f(a) = b.

Range РІР‚вЂњ Range of f is the set of all images of elements of A.

Domain and co-domain РІР‚вЂњ if f is a function from set A to set B, then A is called Domain and B is called co-domain.

means f is a function from A to B, it is written as If b is the unique element of B assigned by the function f to the element a of A, it is written as f(a) = b. A is called Domain of f and B is called co-domain of f.

Mathematics | Rings, Integral domains and FieldsР”Р„ function f from A to B is an assignment of exactly one element of B to each element of A (A and B are non-empty sets).

Mathematics | Independent Sets, Covering and Matching.

Mapping onto vs one to one series#

Mathematics | Sequence, Series and Summations.Mathematics | Generating Functions РІР‚вЂњ Set 2.Discrete Maths | Generating Functions-Introduction and Prerequisites.Mathematics | Total number of possible functions.Mathematics | Classes (Injective, surjective, Bijective) of Functions.Number of possible Equivalence Relations on a finite set.Mathematics | Closure of Relations and Equivalence Relations.Mathematics | Representations of Matrices and Graphs in Relations.Discrete Mathematics | Representing Relations.Mathematics | Introduction and types of Relations.Mathematics | Partial Orders and Lattices.Mathematics | Power Set and its Properties.Inclusion-Exclusion and its various Applications.

Mathematics | Set Operations (Set theory).Mathematics | Introduction of Set theory.ISRO CS Syllabus for Scientist/Engineer Exam.ISRO CS Original Papers and Official Keys.GATE CS Original Papers and Official Keys.