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Part 1 of this article introduces the concept of arithmetic sequence. Like sequences in general, arithmetic sequences can generate what we call arithmetic series. In brief, for every term of an arithmetic sequence there corresponds a partial sum; the sequenceRead More
Consider the following sequences of real numbers. Sequence 1: 2, 5, 8, 11, 14, … Sequence 2: 11, 16, 21, 26, 31, … Sequence 3: 15, 13, 11, 9, 7, … They are examples of what weRead More
In the article Quadratic Functions, we infer the properties of quadratic functions based on given equations of the form f(x) = ax2 + bx + c where a ≠ 0. In the opposite direction, this article describes how to findRead More
In the article Injective and Surjective Functions, the concepts of injective functions and surjective functions are discussed separately. Some functions are injective but not surjective while others are surjective but not injective. In fact, It is possible for a functionRead More
Let f be a function on to given by: The function just-defined is called the absolute value function. For every x ∈ the image of x under f is denoted by |x|. Thus, The graph of the absolute value functionRead More
The set of all natural numbers, , is a countably infinite set. In fact, . Now, let G be the set of all even natural numbers. Thus, G = {2, 4, 6, 8, 10, 12, …}. Note that G isRead More
The readers may find that literatures on mathematics provide various definitions of powers. Some authors do not distinguish the term power from index/exponent. Throughout this article, a power is a mathematical expression in the form of br where . The numberRead More
Definition Let , a, b > 0 and b ≠ 1. The logarithm of a to base b, denoted by , is defined as follows. if and only if The number b is called the base of the logarithm, andRead More
Blindness was not an obstacle for him to deliver magnificent works. Along with his perseverance in studying mathematics, he lost the sight of his right eye and then his left eye as well 31 years later. He discovered a branchRead More
There are times when we need to simplify a square root such as √500 into a simpler form, that is 10√5. Similarly, the form can be simplified to . Additionally, the radical fraction can be simplified to (√5 – √3).Read More