The terms "whole number" and "integer" are often used interchangeably, but they have distinct meanings. Whole numbers are non-negative numbers that don't have any fractional or decimal parts. Integers, on the other hand, include both positive and negative numbers, along with zero, without any fractional or decimal parts.
Here's a breakdown of the key differences:
Whole Numbers:
- Definition: Non-negative numbers without any fractional or decimal parts.
- Examples: 0, 1, 2, 3, 4, 5, ...
- Set Notation: {0, 1, 2, 3, ...}
Integers:
- Definition: All positive and negative numbers, including zero, without any fractional or decimal parts.
- Examples: ..., -3, -2, -1, 0, 1, 2, 3, ...
- Set Notation: {..., -3, -2, -1, 0, 1, 2, 3, ...}
In essence, all whole numbers are integers, but not all integers are whole numbers. Whole numbers are a subset of integers. This means that all whole numbers fit within the broader category of integers, but there are integers that are not whole numbers (like negative integers).
You can think of it like this:
- Whole numbers are like all the people in a specific town.
- Integers are like all the people in the entire country.
Everyone in the town is also a citizen of the country, but not everyone in the country lives in that specific town.
