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Few Concepts in details
(Note: To understand the concept clearly, watch our respective 3D animated videos while reading this article as the illustrations are based on that.)
Function
Objective:
In this session we will understand the concept of a function. We have plotted points on a graph paper. The points are given by their co-ordinates. (4, 5), (-5, 4), (-3.5, -4) etc.
We know that the first number gives us the x-coordinate that is, the distance from origin along x-axis and the second number gives us the y- coordinate that is, the distance from origin along y – axis. It is for this reason that if we change the order of numbers, we get a different point. (4, 5) and (5, 4) are two different points. Such an arrangement of pair of numbers where order is to be retained is called an ordered pair.
The cross product of two sets, AxB = {(a, b) I a e A and b e B} To explore all possibilities let us have two sets. Set A with five robots and set B with seven bikes.
Now we pair a robot with the bike matching its color.
Case I:Green robot with Green bike. Blue robot with Blue bike etc. In this case we find that each robot has only one bike to itself.
Case 2: Let the bike with orange color be replaced with a bike of light green color.
Now we find that the robot with Orange color does not have a bike to itself.
Case 3:Take the bikes of light green and purple color and replaced them with orange colored bikes. Matching the sets again.
Now we find that the Orange colored robot has two bikes to itself. Thus we observe that in the first case each robot from set A has a bike to itself, and there are 2 spare bikes. In the second case there is a robot without a matching bike and finally in the third case we have a robot that has more than one matching bike. These conditions lead us to the definition of a function.
A function is a subset of the cross product of two non-empty sets A and B such that every element of set A has a unique image in set B.
The function is represented by small letters, for example, Function f:A->B. Set A is called Domain and set B Co domain. This further implies that no element of A can have more than one image in B. And also there should not be any element of A which does not have an image in B.Mathematically it implies that no two ordered pairs will have the same first element.
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