March 2014 – Fruits of procrastination

Inductive sets

Inductive sets are sets such that 1. , where is the inductive set under consideration. 2. , where Natural numbers (here, natural numbers include ) are those sets that are present in every inductive set. Let us explore this strand of thought more. Clearly, belongs to every inductive set. Hence, it also belongs to theContinue reading “Inductive sets”

Another rant on undergraduate Algebra

Far too much of Algebra is infested with “equivalence relation” and “well-defined mappings” and what not. Over time, I had grasped their essence, but faltered when trying to fathom their motivation/put them in context. I’m sure you’ve felt the same way in undergraduate Algebra. Then I made the best decision of my life: I startedContinue reading “Another rant on undergraduate Algebra”

A rant on the null-set.

This as a post was long due. What exactly is ? It is the single most confusing thing I have come across. I am going to try and elaborate its properties. I’m going to build the theory in stages. 1. Nothingness. Let us give it a symbol- . This is an element of EVERY set.Continue reading “A rant on the null-set.”