Miscellaneous

I was freshman when I was first introduced supremum and infimum. I could not understand a thing, yet everybody seemed to understand. I felt like stupid, inadequate and also insufficient person to learn mathematics. However, reality is not like that. In truth, I was the one to blame; I hadn’t dived deep into these topics deeply enough. I do not know if I am alone or not, but I think supremum and infimum are the topics which cannot by bypassed without learning and embracing. Today I want to show an interesting fact; if a set has least-upper-bound property and bounded below, then it has infimum. But first let us define supremum and infimum. ...

First Initiation When we first started to learn mathematics, our concern is only to solve problems, understand what equation means, comprehend what teacher says during class and etc. At high school we learn more about sets and functions. However, if we are not curious enough, then the philosophical meaning of the word “mathematical space” is not emphasized. When $f: \mathbb{R} \rightarrow \mathbb{Q}$ is written, everybody who has learned high school math can say “the function takes values from $\mathbb{R}$ and maps it to $\mathbb{Q}$. But have people reading this ever thought about the background? ...