Set Definition

1.       So, sets are really simple to explain and people to understand. But do we really understand what sets are?

2.       In simple words, sets are collection of anything defined by rules such that the rules can clearly tell us whether to put a thing to that set or not.

3.       But what this “anything” is? Basically, what is the “thing” that we are talking about? Are they objects? Why such a concept like set has come into existence? How is it helping us in Mathematics or in any other part of our life?

4.       Let us consider one example; your family is a set. How? It consists of your family members (a rule) and at any point of time you or any of your friends or family can, without ambiguity, decide who is your family member is and who is not.

5.       Even for defining a set, we need to have some particular knowledge about the things that makes the set.

6.       If you give the above definition of the set to a total stranger. Well, that person can’t decide who your family member is or who is not, because he doesn’t know about your family.

7.       So for that person, it is not a set. Once he is provided with the knowledge about your family, then only he can realize that this is a set.

8.       Hence, in Mathematics also when we are defining a set, we should know about the numbers. This knowledge is assumed to be possessed by everyone (but we can’t prove this mathematically ;))

9.       Now coming to the decision about classifying something to a set. The rule says members of your family, so by the knowledge of what makes a family member is basically checking if that member is in relation to you. The relation can be sister, brother, mother or father.

10.   The rule is basically, is a collection of relationships that can be possible between you and any of your family members.

11.   Now coming to what “things” can make a set, it will amaze you that the point 10 above is also a set! J

12.   Well, you are getting to know about Sets!