Natural Numbers and Zero
Note: In mathematics, there are two conventions about whether \(0\) is considered a natural number. In this topic, we will explore both approaches.
1. What are Natural Numbers?
Natural numbers are the numbers we use for counting objects in everyday life.
Definition (in school curriculum):
Natural numbers are the numbers \(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, \dots\) and so on to infinity.
The set of all natural numbers is denoted by the symbol \(\mathbb{N}\):
\(\mathbb{N} = \{1, 2, 3, 4, 5, 6, \dots\}\)
Note: in more advanced mathematics, another notation is sometimes used:
\(\mathbb{N}_0 = \{0, 1, 2, 3, 4, 5, \dots\}\),
where zero is also considered a natural number.
Natural numbers are the numbers \(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, \dots\) and so on to infinity.
The set of all natural numbers is denoted by the symbol \(\mathbb{N}\):
\(\mathbb{N} = \{1, 2, 3, 4, 5, 6, \dots\}\)
Note: in more advanced mathematics, another notation is sometimes used:
\(\mathbb{N}_0 = \{0, 1, 2, 3, 4, 5, \dots\}\),
where zero is also considered a natural number.
Why are they called "natural"?
- The word "natural" comes from the Latin word "natura" — nature
- These are the most natural numbers for humans
- We use them every day: counting apples, books, days, people
- These are the first numbers that people started using thousands of years ago
Examples from life:
- 🍎 Counting apples: 1, 2, 3, 4, 5...
- 📚 Numbering pages in a book: 1, 2, 3...
- 👥 Counting students in a class: 1, 2, 3...
- 🏠 Numbering houses on a street: 1, 3, 5...
- 📅 Counting days in a month: 1, 2, 3...
2. The Natural Number Sequence
The natural number sequence is all natural numbers written in order from smallest to largest.
Important properties of the natural number sequence:
- Infinity: the natural number sequence never ends, there is no largest natural number
- Order: numbers follow strictly in order: 1, 2, 3, 4, 5, ...
- Next number: every natural number has a next number (1 more)
- Smallest number: the smallest natural number is 1
Interactive visualization — available in the full lesson