Background Set Theory is considered to be of primary importa

Background
Set Theory is considered to be of primary importance in mathematics. A Set Theory course is often the prerequisite for advanced undergraduate math courses. If it is not, then the courses themselves often begin with a unit on Set Theory.

Question
Why do you think this is? What makes sets so important? What do sets have to do with numbers? With databases? With proofs?

Solution

Human beings are endowed with the capacity to group things and segregate. That is why men or species or regions were grouped according to some specific criteria by the ancestors. Even a common man likes to sort his clothes groups his favourable songs separately, etc.

This idea of sorting out data or events into groups underlies the main concept in modern Mathematics.

No field of mathematics could be described nowadays without referring to some kind of abstract set

An algebraist may work with a set of equations or a set of matrices.

A statistician typically works with large sets of raw data.

Probability is easily understood by intersection union mutually exclusive etc.

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Numbers are grouped as integers, real, rational whole numbers etc. and subsets give a clear ready picture about which set is contained in which. Thus whole number theory uses sets as bases, and also domain and range of any function is represented by intervals which are also sets.

For data bases, set theory helps to sort data according to required category and further studies can be done.

For proofs, regarding probability for example, set theory is used to explain about total prob = 1, universal sets, mutually exclusive, etc.