Mymathware Shafii's math academy

INTRODUCTION TO REAL ANALYSIS Today i will be treating some problems in real analysis I, problems like the field axioms, countable sets, infinite set…

Phtoto Credit: purch.com MAT206 2015/16 Past Question Check out my post on " Introduction to the real number system[Algebraic structures] " for …

Open, closed and clopen sets Given any nonempty set, we can determine if the elements of the sets are open, closed, clopen, not open, or not closed. This aspects is …

Problem and solutions in convergent sequences I will be sharing some solutions to problems on convergent sequences which i solved earlier today. This is going to be one…

The Co-finite Topology on X is discrete if and only if X is finite This is a very important theorem of the cofinite topology, understanding theorems and proofs sho…

The finite-closed or co-finite Topology Still on general topology, today i will be writing on a very special type of topology called the co-finite or finite closed t…

Principle of  Mathematical  Induction   This is the definition, theorem and proof of the mathematical induction for Real Analysis tutorial. The principle of mathema…

The Triangular Inequality Theorem: The triangular inequality states that if $a$ and $b$ are any two real numbers, then $|a+b|\leq{|a|+|b|}$.............(1) Proo…

The Absolute Value In my previous tutorial on MAT206[Intorduction to Real Analysis], i gave an introduction to the real number system with the algebraic structure in …

Discrete and the Indiscrete Topology Today i will be giving a tutorial on the discrete and indiscrete topology, this tutorial is for MAT404(General Topology), Now in…

Introduction to Real numbers $\mathbb{R}$ Today i will be giving a brief tutorial on the real numbers and its algebraic structure for MAT206(Real analysis I) course. Fo…

TOPOLOGY The study of topology and its spaces is an important aspect of mathematics,topological spaces like other mathematical spaces have axioms that must be satisf…

How To Calculate The Riemann Sums Still on the topic of the Definite Integral, today i will be giving examples on how to calculate the Riemann sums. the Riemann sums…

Understanding The Integral Calculus over the past few weeks i have received many emails from various people asking me to solve some questions and abstract problems o…

Example of Monotone Sequences In my last post, i explained  the monotone sequences and their criteria of convergency,now i will be a giving solutions to problems of …

The Monotone Convergence Criterion The monotone sequence is one important aspect of sequences . A monotone sequence is any sequence ${s_n}$ that is either increasin…

The Limits of absolute Values Today i will be posting about a further theorem that is an order property of the limits of sequences.yesterday i talked about a theorem…

22 operation Properties of Infinity they will not teach you in class The Real number system is so diverse that sometimes you will think it is the largest set of numb…

Analysing The "Squeeze or sandwich Theorem" of sequences . Still on the topic of sequences, i want to discuss on a property of the limits of sequences,which i…

Solution To Problems of Convergence Sequence using Epsilon Approach In one of my previous post titled "The convergence Sequence" i discussed about how to i…