INTEGERS AND ABSOLUTE VALUES
Types of Integers:
1. Positive Integers (Natural Numbers):
Definition: Positive integers are whole numbers greater than zero.
Symbol: N+ or simply N
Examples: 1, 2, 3, 4, ..
2. Negative Integers:
Definition: Negative integers are whole numbers less than zero.
Symbol: N-
Examples: -1, -2, -3, -4, ..
3. Non-negative Integers:
Definition: Non-negative integers include zero and all positive integers.
Symbol: N U {0}
Examples: 0, 1, 2, 3, ..
4. Non-positive Integers:
Definition: Non-positive integers include zero and all negative integers.
Symbol: {0} U N-
Examples: 0, -1, -2, -3, ..
5. Even Integers:
Definition: Even integers are divisible by 2, meaning there is no remainder when divided by 2.
Symbol: {…,-4,-2,0,2,4,…}
Examples: -6, -4, -2, 0, 2, 4, 6, ..
6. Odd Integers
Definition: Odd integers are not divisible by 2, meaning there is a remainder when divided by 2.
Symbol: {…,-5,-3,-1,1,3,5,…}
Examples: -5, -3, -1, 1, 3, 5, ..
7. Prime Integers:
Definition: Prime integers have exactly two distinct positive divisors: 1 and the number itself.
Symbol: {2,3,5,7,11,13,…}
Examples: 2, 3, 5, 7, 11, …
8. Composite Integers:
Definition: Composite integers have more than two positive divisors.
Symbol: {4,6,8,9,10,12,…}
Examples: 4, 6, 8, 9, 10, ..
9. Rational Integers:
Definition: Rational integers are those that can be expressed as a fraction of two integers, where the denominator is not zero.
Symbol: \(\overline Q \) (the set of rational numbers)
Examples: \(\frac{3}{4}\), \(- \frac{2}{5}\), 7 (since 7 can be written as \(7\over 1\)
10. Irrational Integers:
Definition: Irrational integers cannot be expressed as a simple fraction and have non-terminating, non-repeating decimal expansions.
Symbol: I (the set of irrational numbers)
Examples: \(\sqrt 2 ,\,\pi ,e\)