A negative number is any real number less than zero, while a negative integer is a whole number less than zero. This means all negative integers are negative numbers, but not all negative numbers are negative integers.
Understanding the Difference
The key distinction lies in the type of number we're considering.
Negative Numbers
- A negative number is any real number that is less than zero. This includes:
- Negative fractions (e.g., -1/2, -3/4)
- Negative decimals (e.g., -0.5, -3.14)
- Negative irrational numbers (e.g., -√2, -π)
- And of course, negative integers (e.g., -1, -2, -3)
Negative Integers
- A negative integer, according to the reference text, is a whole number that is less than zero. Whole numbers include zero, as well as positive and negative numbers. These are numbers without any fractional or decimal part. Examples include:
- -1
- -2
- -3
- And so on, extending infinitely in the negative direction.
Comparison Table
| Feature | Negative Number | Negative Integer |
|---|---|---|
| Definition | Any real number less than zero. | A whole number less than zero. |
| Examples | -0.5, -1/4, -π, -1, -2 | -1, -2, -3, ... |
| Includes Fractions | Yes | No |
| Includes Decimals | Yes | No |
| Includes Irrationals | Yes | No |
| Relationship | All negative integers are negative numbers. | A subset of negative numbers. |
| From Reference | Every real number other than zero is either positive or negative. | The positive and negative whole numbers (together with zero) are referred to as integers. |
Practical Insights
Think of it this way: Imagine a number line. Negative numbers cover everything to the left of zero, including all the points between the whole numbers. Negative integers are only the whole number points to the left of zero.
In summary
A negative integer is a specific type of negative number. All negative integers are negative numbers, but the reverse is not true.
