[By the one whose mathematical senses have superseded his electron-ic]

Mathematics, they say is the study of sets and functions; I beg to differ. Mathematics is the study of sets only!

Sets, relations and their mappings have bored me and must have bored many of you during the good old schooling days; a few sets were given and their union, intersection, difference, symmetric difference was told to calculate till the point of utter boredom. But that was school mathematics then…..A student good at factorizing quadratics was considered to be a mathematical prodigy. Things are different now, at least for me, now that I know that sets exist and can be made to put in a better use for humanity.

What is a set? Quite a dumb question, if the answer is – A set is a collection of objects. Now, what is a mapping? It is a relation that links elements of a set on to (I won’t use “onto”) another. Now, why is mathematics not a study of functions?
If that were true, then a function must be a set, for then mathematics would be a study of purely sets. The question now is, how is a function f : A -> B, a set? Simple. It is the set of all ordered pairs {a,b}, where a and b belong to the sets A and B.

Now what about all the seemingly non-set-related stuff that has been injected into us? Well, the algebra of polynomials and variables is a special class (class is a collection of sets) of Euclidean rings (rings are sets with special properties) and the calculus is largely included as a set of Lebesgue-integrable functions over the domain of real numbers (real numbers form a field, again a set with special properties).

Think of all the mathematics that you have read or studied, and to explain it unambiguously, you undoubtedly have to resort to SETS!