The set of positive integers, denoted as Z+, is the collection of all whole numbers greater than zero.
Understanding Positive Integers
Positive integers are the numbers we use for counting, starting from 1 and extending infinitely. They are also known as natural numbers.
- They do not include zero.
- They do not include negative numbers.
- They do not include fractions or decimals.
Representation
The set of positive integers (Z+) can be represented in several ways:
- Set Notation: Z+ = {1, 2, 3, 4, 5, 6, ...}
- Description: All integers greater than 0.
Key Characteristics
- Infinite: The set of positive integers is infinite, meaning it goes on without end.
- Discrete: The set consists of distinct, separate values (i.e., there are no numbers between consecutive integers).
- Ordered: The numbers in the set have a natural order from smallest to largest.
Examples
Here are some examples of positive integers:
- 1
- 10
- 100
- 1,000,000
Here are some examples of numbers that are not positive integers:
- -1 (negative integer)
- 0 (zero)
- 1.5 (decimal)
- 1/2 (fraction)
Why is it important?
The set of positive integers is a fundamental concept in mathematics. It forms the basis for many other mathematical ideas and is used extensively in areas such as:
- Number Theory
- Combinatorics
- Computer Science
