Algebra and Topology

Posts and Articles on Algebra, Metric Spaces and Topology

When nothing is everything in Set theory

In an earlier post, I discussed the basic and most important aspects of Set theory, Functions and Real Number System. In the same, there was a significant discussion about the union and intersection of sets. Restating the facts again, given a collection $\mathcal{A}$ of sets, the union of the elements of $\mathcal{A}$ is

Real Sequences

Sequence of real numbers A sequence of real numbers (or a real sequence) is defined as a function $f: \mathbb{N} \to \mathbb{R}$ , where $\mathbb{N}$ is the set of natural numbers and $\mathbb{R}$ is the set of real numbers. Thus, $f(n)=r_n, \ n \in \mathbb{N}, \ r_n \in \mathbb{R}$ is a

Set Theory, Functions and Real Numbers

These study notes on Set Theory, Functions and Real Numbers were written by Gaurav Tiwari when he was studying as a Math undergraduate in 2012-2013. The language is sought to be simple and easy to understand. Further reading material is also provided with this article. If you have any questions, feel free to send a