Activity

In topology we often think about what things look like. But fundamentally, these are mathematical objects and the jump to visualization is not trivial.

We often think in topology of gluing two different points […]

If one is familiar with line integrals from calculus, one may have encountered vocabulary used in theorems to describe regions such as **open** and **closed**, **connected** , and **simply connected**. These all […]

Almost everyone has, at some point, played with the deceptively simple puzzle that is a Rubik’s cube. Even before studying pure maths, we had heard about the idea of Group Theory through an interest in Rubik’s Cub […]

Chúng tôi là sinh viên năm thứ mười hai ở trường học viên quốc gia quận Morris. Chúng tôi học toán thuần túy. Brendan Halstead là thày giáo của chúng tôi.

In algebra we are interested in thinking about objects. Objects can be many things including numbers, sets, and many more complicated constructions. Category theory is a powerful tool which analyzes these objects […]

Can you get a room in an infinitely large, yet fully booked, hotel? There are a lot of rooms to count in Hilbert’s Grand Hotel, an infinite number of them to be exact. A common understanding of infinity is that i […]

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{width=”paperwidth”
height=”paperheight”}; […]

I’ve decided to migrate the content of the blog [here](https://rmehtany.github.io/notes/AlgebraicGeometry/) as I wasn’t particularly happy with the styling and features of the site. Be sure to check it out!

Basic Special Functions are Absolute Value Function, Signum Function, Floor and Ceiling Functions, Fractional Part Function and Integer Function.

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hline text { notation } & […]

Let $ (x_n) $ be a sequence of reals.

$ p in mathbb{R} $ is an accumulation point of the sequence if for every $ epsilon > 0 $, $ x_n $ lies in $ (p-epsilon, p+epsilon) $ for infinitely many $ n $ […]

Let $ S $ be a set. Recall a partition of $ S $ is a collection of non-empty pairwise disjoint subsets with union $ S$.

Any partition $ P $ of $ S$ gives a relation $a sim_P b stackrel{text{def}}{iff} ( a, […]

::: {.lemma}
**Lemma 1**. *Suppose $E$ is a Riesz space, $F$ is an order ideal of $E$
and $(f_i)_{iin I}$ is a net in $F$. Then $f_i$ converges (in order) to
an element $f$ in $F$ iff and only if $f_i$ […]

Welcome to the blog Infinity!

Before anything else, we will start with definitions.

– **Antiderivative**
> Given a well-defined function $f$ on an interval $[a,b]$, the antiderivative of $f$, which we denote as $F$, is also a function […]

# Notes

This was a beamer slideshow that [badly] converted into a more text like format. This was also meant for a “maths talk” I did on how to introduce homeomorphisms in a more interesting way.

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# Initial Notes

These notes were also written in December 2020 just as I started to figure out how to use $LaTeX$, and started to write things related to math. This was actually used in a Youtube video I […]

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