An understanding of healthy relationships is a must for a peaceful and happy life, and so is the understanding of mathematical relations necessary for a student to lead a happy academic life. If you feel confused or are not clear about the concept of a mathematical relation and a function, then you certainly need to read this article with concentration.
A relation in the mathematical sense can simply be defined as a set of ordered pairs of objects. The collection of first objects in each pair forms the domain of the relationship; while the collection of second objects forms the range. There is no uniqueness in the relationship unlike a function as will be seen later on. Take a simple example in that you have an ordered pair where you name is written first and then you shoe size is written. Any number of people can have your shoe size and you cannot do anything about it, but if it is a function you certainly can.
A function is similar to a relation with the exception that each element in the domain has got a unique value corresponding to the same in the range. In other words a function can be said to be a strictly defined relationship, like human relations in a civilized society as compared to a barbaric society.
This leads us to the corollary that – ALL FUNCTIONS ARE RELATIONS BUT THE REVERSE MAY NOT BE TRUE ALWAYS.
Technically a function could then be defined as a relationship between two quantities A and B, where any value assigned to A, gives a corresponding value for B, then B is said to be the function of A.
The quantity A in the above case is also known as a dependant variable, while B is known as the independent variable; due to the obvious reason that a change in B causes a corresponding change in A.
A function of the above type can be mathematically written as A = f(B) which can be read as – “A is a function of B”
Given above is the most basic situation where there are only two variables but in real life there can the more than two variables in a function as well. Take the example of the volume of a sphere which depends on its radius only, but the volume of a cylinder depends not only on its radius but its height as well hence it is a function with three variables. Similarly there can be functions with more than three variables as well.
In case of human relationship no matter how well behaved or good the relationship is between two people, there are certain limits to which the relation can be strained otherwise it breaks up. Similarly mathematical relations have their limits and they form the very basis of an interesting branch of mathematics namely calculus, but we will take it up in another article.
