Hello friends of steemit in this publication I will be starting with a series of articles related to fundamental mathematics, that is, the necessary bases for a more complex understanding of this prestigious area, in this case I will start with the sets.
Mathematics in the search for the logic of our environment has always taught us to trust in its wisdom, therefore, it is indisputable each of the forms of teaching that at all levels gives us this wonderful numerical and abstract science, we can affirm then that this wonderful idea of achieving to group objects of the same nature has allowed us a wide classification of them, allowing with this the understanding of the same mathematics now in a much more practical and precise way.
In education, this set tool makes it easier for us to easily transmit generalized examples to our students, this has been possible due to the familiarization of such term, since we can say then that when speaking together we are referring to a certain collection of things or objects, they are formed by parts called elements or members of a certain set.
In mathematics when talking about sets we have related to the conformation of elements whose properties are related to each other, for example, when we group or classify numbers in pairs or odd, natural or integers, or simply by saying that any of our hands represents a set whose elements are your fingers, to put a practical example and simple, the set can generally be represented with uppercase letters and their elements with lowercase letters:
N is the set and a, b, c, d, e, represent the elements of N, that is, the fingers of one of our hands.
It is important to note that when an element is part of a set, we say that such an element belongs to the respective set, and if on the contrary it does not belong to it, we express the opposite, we use the following symbols to represent the exposed:
For example: Set B is represented by all preschool children:
How could we define a set?
We can do this when we know exactly the elements that belong to it, therefore, we say then that the definition of a set is possible when we can name all the elements that make it up; we say that it is defined by extension or enumeration, but we could also characterize it using a certain property which allows us to affirm whether a certain element belongs to that set or not, for this case we say that this set is defined by understanding or ownership.
For example; we could take the exercise to start the fingers of one of our hands, therefore it would be expressed as follows, by extension:
We could also say that it is defined by understanding:
This we can read; The set represented by M is made up of all the elements x such that x is a finger of the hand.
This last form or way of expressing a set is the most useful because most sets have many elements making it difficult to name them all individually, that is why we resort to the general property of the elements, that is, define the set by understanding, for example:
The set C; represented by the integers greater than 4, we can notice that expressing this set by extension will be very complicated because of the large number of elements that belong to that set, therefore, we must do it by understanding then we have:
We read this, The set C represented by the numbers x such that (/) x belongs to the integers (Z) that are greater than 4.
Until the next publication where I will be expanding this important topic as are the sets which we use in different areas of our lives.
Notes: All the images were created with the help of Microsoft Power point 2010 for Windows 7.