Question

Describe the set of numbers that are real numbers that cannot be expressed as one integer divided by another would it be negative or rational or improper

Answer 1

The set of real numbers that cannot be expressed as the quotient of one integer divided by another integer is primarily made up of **irrational numbers**.

### Breakdown:

1. **Rational Numbers**: These are numbers that can be expressed as the quotient of two integers (i.e., \( \frac{a}{b} \), where \( a \) and \( b \) are integers and \( b \neq 0 \)). Examples include \( \frac{1}{2}, 3, -4.5, 0, \) and \( 7 \). All rational numbers can be either positive or negative.

2. **Irrational Numbers**: These are real numbers that cannot be expressed as a fraction of two integers. Examples include \( \sqrt{2}, \pi, e, \) and any non-repeating, non-terminating decimal.

### Characteristics:
- **Irrational numbers** are not negative or positive by definition, as they can belong to either set.
- They are a subset of the **real numbers** that do not have a representation in the form of \( \frac{a}{b} \) (where \( a \) and \( b \) are integers).

### Conclusion:
Thus, the set of real numbers that cannot be expressed as one integer divided by another specifically refers to **irrational numbers**, which can be either positive or negative.