Set Theory

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{Definition 1.1.:} $ A set is a collection of objects called elements ...