Elements Of Mathematics Class 12
Welcome to the world of mathematics. In this article, we’ll introduce you to some of the basic concepts of mathematics.
Integers are the numbers that can be written as fractions with no remainders. Integers include natural numbers (1, 2, 3), whole numbers (1, 2, 3) and their opposites (-1,-2,-3).
The set of integers is infinite. An integer can also be expressed as an algebraic expression where each term has a variable raised to a power that is greater than 1. For example:
- 4a + 5b = 4a+5b = 4a + 5b = 4ab
The set of rational numbers includes all whole numbers, integers, and decimals. It is the largest collection of numbers that can be written as a fraction. This means that if you divide one rational number by another rational number, you will get an integer (a whole number) as the answer.
The denominator of a rational number must not be zero; otherwise it is an infinite quantity which cannot be represented by any finite quantity such as a fraction or decimal value.
Similarly for the numerator: it must not equal zero either because this would mean there could never be any positive values added together to make up this value!
In mathematics, the term “irrational” is used to describe a number that cannot be written as a fraction. It is an adjective that can be applied to any real number–not just integers or non-zero decimals. An example of an irrational number is pi (3.14159265358979323846264338327950288419702…), which cannot be written as a fraction because it never ends and doesn’t contain any repeating patterns.
Irrational numbers are important because they help us understand things like circles, ellipses and other geometrical shapes without having to define them with specific values such as 2 or 3 inches long or 5 cm wide. These shapes only exist because there are infinite points along their perimeter; we wouldn’t be able to draw these objects if every point were given its own value!
Real numbers are the set of all possible numbers that can be expressed as a ratio of two integers. They include rational and irrational numbers, but not transcendental numbers (such as pi). Real numbers were first conceived by Pythagoras and Euclid in the 5th century BC, who defined them as ratios to their simplest terms; however they did not explicitly define an operation on these ratios that would satisfy all properties expected from an algebraic structure at this time. This was finally achieved by Carl Friedrich Gauss in 1799 with his discovery of arithmetic operations on complex quantities, which led him to create the first theory about complex analysis and its applications in geometry and physics.
Complex numbers are numbers that can be expressed as the sum of a real number and an imaginary number. The real part is called the “real” part, and the imaginary part is called “imaginary”.
The imaginary number is written as a lowercase letter i. In other words, 1 + 2i = 3 + 4i
In this article, you learned about the elements of mathematics. In particular, we looked at integers, rational numbers and real numbers. We also saw what complex numbers are and how they relate to other types of numbers.
We hope that this article has been useful for you in understanding these concepts!
In this article, we have looked at the basics of real numbers and complex numbers. We hope that you have gained some insight into how these concepts work and what they mean for mathematics as a whole.