The number system is the foundation of mathematics. It encompasses various types of numbers that we encounter in our daily lives. In this article, we’ll explore the key concepts related to the number system, including natural numbers, whole numbers, integers, rational numbers, irrational numbers, prime and composite numbers, divisibility tests, finding remainders, and surds.
Natural Numbers
- Definition: Natural numbers are the positive integers starting from 1 and continuing indefinitely (1, 2, 3, 4, …).
- Use: They represent counting or ordering.
Whole Numbers
- Definition: Whole numbers include zero along with all the natural numbers (0, 1, 2, 3, …).
- Use: Whole numbers are useful for counting objects or quantities.
Integers
- Definition: Integers include positive numbers, negative numbers, and zero (…, -3, -2, -1, 0, 1, 2, 3, …).
- Use: Integers are essential for representing both positive and negative quantities.
Rational Numbers
- Definition: Rational numbers can be expressed as a fraction (p/q), where p and q are integers and q is not zero.
- Use: They represent ratios, percentages, and fractions.
Irrational Numbers
- Definition: Irrational numbers cannot be expressed as a simple fraction. Examples include √2, π (pi), and e.
- Use: They appear in geometry, trigonometry, and other mathematical contexts.
Prime and Composite Numbers
- Prime Numbers: These are natural numbers greater than 1 that have exactly two distinct positive divisors: 1 and the number itself (e.g., 2, 3, 5, 7, 11).
- Composite Numbers: These are natural numbers greater than 1 that have more than two positive divisors (e.g., 4, 6, 8, 9, 10).
Divisibility Tests
- Divisibility by 2: A number is divisible by 2 if its last digit is even (ends in 0, 2, 4, 6, or 8).
- Divisibility by 3: The sum of the digits should be divisible by 3.
- Divisibility by 5: The number ends in 0 or 5.
- Divisibility by 9: The sum of the digits should be divisible by 9.
Finding Remainders
- When dividing one number by another, the remainder is what’s left after the division process. We use different theorems to find remainders of complex expressions involving powers.
Surds
- Definition: Surds are irrational numbers expressed in the form of √n, where n is a positive integer. They appear in algebra and geometry.
Conclusion
Understanding the number system is crucial for solving mathematical problems. Remember these key concepts, and you’ll be well-prepared for the CDS and AFCAT exams. Happy studying!
