We perceive several problems related to the functions in many situations in life and develop solutions accordingly. The function shows the effect of one (or more) variable(s) on another variable. In simple terms, one factor can be called the transformation of another factor. When you send a piece of mail by cargo, you pay according to the weight of your cargo. Or imagine using an hourly Internet service in a library or airplane; the more hours you use the Internet, the more you pay.
A group of people want to rent a bus. The number of people does not affect the cost of rent for a bus. However, the cost per person could change depending on of the number of people. The more passengers, the less fee they pay for each passenger. Conversely, if the number of passengers is less, the cost of the bus fee could be more.
The examples are given above help to understand the mathematical function more easily. We perceive several problems related to the functions in many situations in life and develop solutions accordingly. The function shows the effect of one (or more) variable(s) on another variable. In simple terms, one factor can be called the transformation of another factor.
Consider shipping by mail. There are actually two situations here; the weight of the cargo sent and the amount of money paid based upon the cargo’s weight. This gives us a hint for the payable amount. For example, we may know how many pounds of cargo can be sent for $10. We also may calculate how much money is needed to ship 5 pounds of cargo. We can formulate this shipping problem: Let x be the weight of the cargo and let y be the amount to be paid. In addition, for each parcel sent, including taxes, let us assume that it costs $3. In this case, we get an equation such as y = 2x + 3. Here, the number 2 given in front of the variable x is the money paid per pound. We calculate how many dollars we will pay for a 4-pound cargo: (2x4) + 3 = $11. If 2 dollars per pound is received, a 4-pound package shipping fee is 11 dollars.
Another example would be the use of the Internet. If 40 cents is requested per hour, $1.2 will be given for 3 hours of internet usage. Thus, the equation can be written as y=40x, where x is internet usage time per hour, y is amount to be paid.
The bus rental example is slightly different from the above two examples. Although this example specifies the function, this time there is a reverse situation. In the first two examples, like (x or) input increases, (y or) output will increase. In the case of bus rental, the bus rental fee is fixed and as the number of passengers increases, the payment per person will decrease. Let’s say $400 is required for the daily rental of a bus. 40 people pay $10 per person while 8 people pay $50 per each person. This equation would be; y=400/x, where x is the number of people, y is the amount of money paid per person. Functions are important in understanding the relationship between two variables.
Life is a function. In mathematics first, what is the function in its simplest form? Let us give the known definition in schools.
Function: Let A and B be two sets different from the empty set and there is a relation f from set A to set B. If the relation f associates each element of the set A to one and only one element of the set B, this relation is called the function from set A to set B. It is shown as f: A→B or A→B. A is called the definition set of the function and B is called the set of values. A set of elements that match the elements of set A in set B is called the set of images of the function and is denoted by f (A).
In this case, if we clarify the definition a little, a relationship from A to B to be defined in order to function f; the following conditions must be met:
- There should be no elements in the definition set that do not have an image. However, the element can remain exposed in the value set.
- Each element in the definition set must not have more than one image.
Let us try to find the reflections of the definition in our lives. We assume that A is the world in which we live. If we say “World” for Set A (Definition Set), we would call Group B “the Afterlife” (Value Set). Because there is a connection from this world to the other world. We will see our values in the afterlife against what we do in this world. As someone who fits the definition of a “good” person will be of high value, the definition of a “bad” person will consequently result in a lower value. So, set A considers the world and its elements as ‘living people’. We can think of all the people in the world and include them in this group since life is finite for all of us. The mathematical meaning of this reality is the following: all elements will be moved from set A to set B (Let A and B be two sets different from an empty set and a relation f from set A to set B.). There is such a connection (or relation) that one who leaves the world cannot go to two places at the same time. Destinations are clear: abode of reward or abode of punishment. We will all be eventually placed into one of these two groups. In some cases, the last stop of the people will be paradise, even if there are those who go to hell first and purify their sins. Consequently, in the last case, no one will be in two places at the same time (If the relation f associates each element of the set A to one and only one of the set B, this relation is called the function from the set A to the set B).
Just because everyone has one final destination does not mean that that destination can only hold one person. If the levels of Heaven and Hell are considered correctly, it is possible that there is more than one person for each level or that no one has come to that level. It is possible that there are those who have sinners at the same level. We can speculate that there may even be such a level that is inaccessible to all people. The Creator creates such places in order to show His grace, mercy, and power. (In the definition set, there should not be any elements without an image. But in the value set, there may be exposed elements.)
Life itself is a function. God created life according to certain rules. We should do our best to explore, find, and use these rules. Seeing the beauties of life and being amazed by the astonishment and capturing happiness in both worlds is achieved by seeing the manifestations of God everywhere.