Mathematics

Introduction In 1931 a mathematician with round glasses wrote a quite short paper with title “Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme”. He was 25 years old. So young was he that, instead of tearing mathematics apart with the energy of his youth, he could have spent his time doing nothing. He was at the University of Vienna and since 1938 a permanent member of the Institute for Advanced Study at Princeton. ...

Back then When I was in college, I used to solve a lot of sequence problems. I really liked the topic. It is something that I cannot depict right now, because I have only a few words in my mind. Whatever I write here cannot express the importance of the sequences in mathematics. Nevertheless, I will try to explain the topic while giving my understanding. While learning sequences it is important to build a bridge between the mathematics we know right know, and the mathematics that we will know in the future. ...

The edges we all know I guess everybody that has a little curious have met with Zeno. It is unclear but generally thought that Zeno paradoxes have been developed to support the Parmenides’ doctrins by Zeno of Elea. Do not worry we will not talk about neither Parmenides nor his absurd motion doctrins. By the way he said that “motion is nothing but an illusion”. However, we will use Dichotomy paradox to address the topics infimum and supremum. Dichotomy paradox basically states that to travel any finite distance, you must complete infinite number of tasks using your finite amount of time, which is a paradox since there’s an infinite number of tasks corresponds to finite time, the journey can never be completed. Here is the process that Zeno followed: first decide a goal. Second go halfway of it and then go half of the remaining distance, and then repeat the process. Having to reach a halfway point goes on infinitely. ...

Build the intervals and stay inside Whenever I talk about mathematics, I directly think of number sets. It is surprisingly hard to build, yet easy to understand. Each of them have a different purpose, there is a very close relation between them. Until we prove the properties and maybe the existence of the number sets we will use $\mathbb{R}, \ \mathbb{N}, \ \mathbb{Z}, \ \mathbb{Q}, \ \mathbb{C}$ without proving the properties, as if we all accept and embrace them. Further, Even I won’t talk about Peano’s axioms. ...

In this blog we use so called LaTeX to represent the mathematical terms. To sustain and maintain the beauty of the mathematics it is SO necessary to use LaTeX. Let’s start with the very well-known definition in mathematics. We will start with definition of a set, some basic properties of sets and operations on sets. Neat start to set theory $ \textbf{\small Definition 1.1.:} $ A set is a collection of objects called elements ...

My Life in a Nutshell When I started school, I was 7. I was thrilled and excited. I learned to read, which I’ve used every day since 😊. I was a fast reader, and I took full advantage of that. But let’s stick to our topic: mathematics. Our primary school teacher was an angry and grumpy man, though I liked him. Could it have been Stockholm syndrome? I don’t know, maybe. ...

Rabbit There was once an old rabbit arrogant, yet elegant who knew nothing of Alice, the girl who would soon chase after him. Rabbit used to make his bow tie every day, wear his suit, quit his hole and finally visit the human’s garden. If he is lucky he would find a pipe and have a good smoke. His mind was always full, and for that very reason, he never jumped. He believed that if he ever jumped, the thoughts in his head would fly away and perhaps he would never find them again. ...