Tag: history of mathematics pdf
Numbers play a significant role in this world, as most situations involve the use of numbers. Numbers are defined as strings of digits used to indicate quantity, size, or measurement. They measure size – how big or small a portion is. There are several types of numbers in mathematics, but they fall into two main classes: counting numbers and scalars. To understand why there are different classes of numbers and what they are, we have to take into consideration how people reach out the familiar number systems and expand our numbers as we gain more knowledge of arithmetic.
Many kids are proud of themselves when they can start counting the numbers or things from one to one hundred. A little later, they will experience awe and wonder when they first recognize that counting goes on endlessly with no limit. These kids have a comprehension of counting and natural numbers, and also with the concept of infinite numbers that means infinity, before they are introduced with the number system. In general, a number system comprises a set of items that can be connected, based on agreed rules, by arithmetic operations, namely addition, subtraction, multiplication, and division, that always produce answers in the set. However, negative numbers and complex numbers were often disparagingly referred to as excessive numbers and imaginary numbers.
The numbers used to measure some quantity to any desired degree of accuracy are called scalars. For example, the height of a pole is 15.38 meters, or the speed of a car is 80.25 kilometers per hour. They can have decimal places or fractional parts. From this example, one thing can be understood that the numbers mentioned above be defined under scalars. These scalars are mainly considered as the real numbers. Real numbers are instrumental in everyday life. Real numbers help us in counting and measuring the quantities of various items. For instance, when we ask the shopkeeper about how many candies we can get for a certain amount of money, they use real numbers when they reply.
In many situations, such as when dealing with financial data or arithmetic operations on numbers in maths, we often use positive and negative numbers, i.e. integers (positive integers and negative numbers) to denote increase or decrease. Also, we know that real numbers can be divided into two types namely rational and irrational. Many people work only on rational numbers to ease their activities and save time, although no rational number provides exact measurements of even simple forms. Thus, precise measurements can be approximated to a high degree of accuracy. For example, the length of the diagonal of a unit square is the square root of 2, and this is an irrational number, i.e., this number cannot be expressed as the quotient of two integers. In other words, these types of numbers have non-terminating non recurring decimal expansions.
In this way, numbers have a primary and very significant role in mathematics. Without numbers it is impossible to imagine maths since every element and parameter in maths comprises numbers. Also, different numbers are used in different scenarios based on the complexity and the purpose.