Describe a set of numbers in a real number that cannot be expressed as an integer divided by another
One example of a set of numbers that cannot be expressed as an integer divided by another is the set of all irrational numbers.
An irrational number is a number that cannot be expressed as the ratio of two integers. These numbers have infinitely long and non-repeating decimal representations. Examples of irrational numbers include π (pi), √2 (square root of 2), and e (Euler's number).
No matter which two integers we choose, we cannot form an exact division that equals an irrational number. For instance, if we take 1 divided by π, it will result in a decimal that never ends or repeats. Similarly, if we take any other integer divided by any irrational number, the result will always be a non-repeating decimal.
A set of numbers in real numbers that cannot be expressed as an integer divided by another includes any irrational number.
Irrational numbers are real numbers that cannot be expressed as a fraction or a ratio of two integers. They have non-repeating and non-terminating decimal representations. Examples of irrational numbers include pi (π), the square root of 2 (√2), and the golden ratio (φ).
These numbers are not expressible as the quotient of two integers, so they cannot be written in the form "integer divided by another integer."