Describe the set of numbers that are real numbers but cannot be expressed as one integer divided by another.

Answer 1

The set of numbers that are real numbers but cannot be expressed as one integer divided by another are numbers that are irrational.

Irrational numbers are those that cannot be written as a fraction (integer divided by another integer) and have decimal expansions that neither terminate nor repeat. They cannot be expressed as a simple ratio of integers. Examples of irrational numbers include √2, π (pi), e (Euler's number), and φ (golden ratio).

These numbers are considered to be non-repeating and non-terminating decimals. They extend infinitely without exhibiting any pattern. As a result, they cannot be expressed as a fraction or in the form of one integer divided by another.