INTEGERS AND ABSOLUTE VALUES
IMPORTANT INFORMATION ABOUT INTEGERS
Odd and Even Patterns:
All integers can be classified as either odd or even.
Odd integers can be represented in the form 2k + 1 where k is an integer
Even integers can be represented in the form 2k, where k is an integer.
Zero as a Neutral Element:
Zero is unique among integers; it is neither positive nor negative.
Adding or subtracting zero from any integer leaves the integer unchanged.
Prime Numbers:
Prime numbers are integers greater than 1 that have no positive divisors other than 1 and themselves.
Examples of prime numbers include 2, 3, 5, 7, 11, and 13.
Composite Numbers:
Composite numbers are integers greater than 1 that have more than two positive divisors.
Examples of composite numbers include 4, 6, 8, 9, and 10.
Sum and Product Rules:
The sum of two even integers is always even.
The sum of two odd integers is always even.
The sum of an even and an odd integer is always odd.
The product of two even integers is always even.
The product of two odd integers is always odd.
The product of an even and an odd integer is always even.
Rational and Irrational Numbers:
All integers are rational numbers because they can be expressed as fractions with a denominator of 1.
Examples of irrational numbers include the square root of non-perfect squares and certain mathematical constants like \(\pi\) and e
Consecutive Integers:
Consecutive integers are integers that follow each other in sequence.
For example, 3, 4, 5 are consecutive integers.