The Calculus

Hi, you don’t have to breathe heavily when you hear the word “CALCULUS”. There is nothing new in field of mathematical calculations and basic sciences that have not been explored before—foundations had been lay. So, we just have to use established theories, rules, principles and formats to navigate our way through. Basically, we have no reason to form our own theory—the mathematical gurus have done that for us. So don’t expect new formulas, except to refresh our minds on the established ones.

MATHEMATICS—SET

Now, let’s begin from a simple arithmetic theory.

SET in mathematics is taken to mean a list of objects, numbers or elements and their properties.

Elements of Set

Some of the basic elements of set can be derive in the following properties through their preliminary definitions:

 Odd Number: this is a number that when divided by two (÷2) leaves a remainder of one (1).

Example: … 3, 5 …

 

Integer: An integer x is said to be a factor of another integer y if x can divide y without leaving any remainder. Example: The set factors of 48 = {1, 2, 4, 6, 8, 12, 24, 48}

 

Even Number: This number leaves no remainder when it is divided by two (÷2).

Example: … –6, 4, 2, 0, 2, 4, 6 …

 

Prime Number: This is any positive number that is exactly divisible only by itself and one.

Example: 2, 3, 5, 7, 11, 13, 17. . .  

 

Prime Factors: The prime factors of a number n refer to the factors of n which are prime numbers.

Example: The set of prime factors of 36 = {2, 3}

 

Multiple Number: multiple of a number x refers to any number formed when x is multiplied by any integer. Example: Multiples of 3 are 3, 6, 9, 12, 16, and so on.

Digest this few basic elements of set; we shall go deeper in subsequent editions.

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