Who invented relations and functions

This means that a set is merely a collection of something which we may recognize. In this chapter, we try to extend the concept of sets in two forms called Relations and Functions. For doing this, we need to first know about cartesian products that can be defined between two non-empty sets.

It is quite interesting to note that most of the day-to-day situations can be represented mathematically either through a relation or a function. For example, the distance travelled by a vehicle in given time can be represented as a function. The price of a commodity can be expressed as a function in terms of its demand.

The area of polygons and volume of common objects like circle, right circular cone, right circular cylinder, sphere can be expressed as a function with one or more variables. In class IX, we had studied the concept of sets. We have also seen how to form new sets from the given sets by taking union, intersection and complementation.

Developed by Therithal info, Chennai. Toggle navigation BrainKart. Home Maths 10th Std Introduction. Relation and Function Gottfried Wilhelm Leibniz also known as von Leibniz was a prominent German mathematician, philosopher, physicist and inventor.

Introduction The notion of sets provides the stimulus for learning higher concepts in mathematics. He says that a curve can be drawn by letting lines take successively an infinite number of different values. This again brings the concept of a function into the construction of a curve, for Descartes is thinking in terms of the magnitude of an algebraic expression taking an infinity of values as a magnitude from which the algebraic expression is composed takes an infinity of values.

Let us pause for a moment before reaching the first use of the word "function". It is important to understand that the concept developed over time, changing its meaning as well as being defined more precisely as decades went by. We have already suggested that a table of values, although defining a function, need not be thought of by the creator of the table as a function.

Early uses of the word "function" did encapsulate ideas of the modern concept but in a much more restrictive way. Like so many mathematical terms, the word function was first used with its usual non-mathematical meaning. Leibniz wrote in August of Johann Bernoulli , in a letter to Leibniz written on 2 September , described a function as In a paper in on isoperimetric problems Johann Bernoulli writes of "functions of ordinates" see [ 32 ].

Leibniz wrote to Bernoulli saying I am pleased that you use the term function in my sense. It was a concept whose introduction was particularly well timed as far as Johann Bernoulli was concerned for he was looking at problems in the calculus of variations where functions occur as solutions.

See [ 28 ] for more information about how the author considers the calculus of variations to be the mathematical theory which developed most intimately in connection with the concept of a function. One can say that in the concept of a function leapt to prominence in mathematics.

Euler defined a function in the book as follows:- A function of a variable quantity is an analytic expression composed in any way whatsoever of the variable quantity and numbers or constant quantities. This is all very well but Euler gives no definition of "analytic expression" rather he assumes that the reader will understand it to mean expressions formed from the usual operations of addition, multiplication, powers, roots, etc. He divides his functions into different types such as algebraic and transcendental.

The type depends on the nature of the analytic expression, for example transcendental functions are not algebraic such as Euler allowed the algebraic operations in his analytic expressions to be used an infinite number of times, resulting in infinite series, infinite products, and infinite continued fractions.

He later suggests that a transcendental function should be studied by expanding it in a power series.

He does not claim that all transcendental functions can be expanded in this was but says that one should prove it in each specific case. However there was a difficulty in Euler 's work which was to lead to confusion, for he failed to distinguish between a function and its representation.

Jahnke writes [ 2 ] :- Until Euler the trigonometric quantities sine, cosine, tangent etc. It was Euler who introduced the functional point of view. References show. H N Jahnke ed. L Atkinson, Where do functions come from? R Bhatia, The development of the concept of a function, Math. Student 63 1 - 4 , - S Bochner, The rise of functions, Rice Univ.

Studies 56 2 , 3 - R Cantoral, Formation of the notion of analytic function Spanish , Mathesis, Mathesis 7 2 , - J Dhombres, The mathematics implied in the laws of nature and realism, or the role of functions around , in The application of mathematics to the sciences of nature Kluwer Acad.

Paris VI, Paris, , 23 - I Kleiner, Functions : historical and pedagogical aspects, Sci.