Mymathware Shafii's math academy

How do you proof $\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}$? It is not always true. To see the clear picture, we solve some clear examples. Remember, $\sqrt{\frac{a}…

What is an ordinal number?  Ordinal numbers was introduced in 1883 by George cantor, it is the process of arranging natural numbers in orderly(increasing or decreasing o…

Fixed points: A self explanatory discussion on fixed points.  Fixed point also known as invariant point is a beautiful concept of mathematics. The fixed point of a funct…

What do we mean when we say a function is asymptotic? Two functions $f(x)$ and $g(x)$ are said to be asymptotic if a binary relation is defined on them as thus: $f(x)\si…

Metric space: Convergence and continuity of metric spaces In metric space, we can not talk about convergence and continuity without applauding Felix Hausdorff for his im…

Metric space: Open and closed Balls, neighbourhood, open and closed set - Lecture II  The distance function provides an idea of the "surrounding" of a point. G…

Metric spaces: An abstract study of distance of elements in a set. The word metric  literally means distance, and metric spaces is the study of distance or a study of ho…

Why can't any number be divided by zero(0)? The mathematicians will tell you that it is really inconvenient to allow division by zero in most algebraic systems, so i…

Homeomorphism: the isomorphisms of topological spaces. When studying topological spaces, you will come across homeomorphisms, in one of my papers, i presented a paper on…

Why is there no negative zero and negative minus? Mathematically, zero is considered neither as a negative nor a positive, because from our  number line we s…

Infinity: The numbers without boundaries. The Infinity can simply be defined as a number without boundary or we say a boundless or endless number that is larger than any…

Ending the mathematical argument behind $0^0$.  $0^0$ is a century problem that many mathematics students find rather disturbing. So many people have proposed their proo…

What is a transcendental number, examples and properties? Happy new year to all my readers and followers. Today, i will be celebrating the new year with you by writing o…

Why the natural logarithm are not as confusing as you think. This is my last post for the year 2020, by tomorrow Jan 1st, 2021, we are going to be marking a new decade, …

Proving the Madhava-Leibniz series for pi(π)  One of the earliest known approximations of $\pi$ was done by an Indian mathematician Madhava of Sangamagrama during th…

Why does pi have a constant value of 3.14159265359...?  can we define other values for pi?  $\pi$ is a lowercase greek letter used as a mathematical constant pronounced …

Why study calculus in real analysis when we can study it in elementary mathematics? Real analysis is an area of analysis that studies concepts such as sequences and thei…

Evaluate the integral $\int{(2x+3)}\sqrt{x-4}dx=I$ Let $3=-8+11$ $\therefore$, $I=\int{(2x-8+11)}\sqrt{x-4} dx$.  $=\int{[2(x-4)}+11]\sqrt{x-4}dx$.  $2\int{(x-4)}^{\fra…

What can one learn from real analysis that is not taught in high school? There's no universal standard for what “real analysis” means as an undergraduate course, nor…

Today i am going to be posting on something related to my current area of research, i am currently researching on the C*-algebras and i will be posting on a v…