I have been reading Topics in Algebra and got really interested when the author says *counting* is sometimes the most difficult part in mathematics. How does one account for all the possible scenarios in complex situations?

I find one mathematical concept which helps a lot in this regard is that of an *equivalence relation*. The most striking (yet basic) result of these equivalence relations is that of the disjointedness of the corresponding *equivalence classes*.

As I read more of the book, I am becoming convinced that I dont have to read it anymore! I dont see why constructing a theory based on a predefined structure of the objects is any good (group theory is built on the notion of a group). Such a theory may have its uses for applications (e.g: Fourier theory) but my tastes are currently towards understanding the limitations of logic itself.

I am done wading through all those endless theorems. I would love to understand *that* Godel’s incompleteness theorem paper now. Ofcourse, that is an adventure in itself.

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