Set theory

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Set theory is defined as a collection of well defined objects. These objects are called elements. Here the main emphasis lies on the word 'well defined'. What is the meaning of well defined? The meaning of well defined is that everyone should agree with the concept that the particular object or element is included in the collection. If the opinion differ from person to person about the inclusion of that particular object or element then that collection can't be defined as a set.
Let us take some examples so that you can clearly understand the definition.

  1. The set of all the students of JNU.
  2. The set of the rivers of India.
  3. The set of oceans of the world.
  4. The set of IIT's of India.
  5. The set of national parks of India.
All these are called set because here everyone agree about the particular object. In the first example, you can easily say whether the students X,Y,Z are from JNU or not. Either he or she is a student there or not. There is no biasness about that.
In the second example if I say the Ganga is included in the set, then everyone have to agree with me. But if I take the name of the Amazon river, then this element is not included in the collection and again everyone have to agree with me because Amazon is not present in our India.
In the third example it is also a set because there are five oceans in our world.
Likewise example 4 and 5 are set because they are well defined.
Now I will mention some examples which are not set.

  1. The set of cute boys in Delhi.
  2. The set of talented girls in Goa.
  3. The set of beautiful models in Lakme' fashion week.
In the first example cuteness if vary to person to person. The facial features that I am finding cute maybe you will not agree with me. So I can find Kartik Aryan is cute, maybe you don't find him cute. Or you can find Siddharth Malhotra is cute, but  may be not by me . So for a particular element if everyone is agree then it is a set and if there is at least one person who is not agree and he/she has a solid logic behind the disagreement then this is not set.

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