Let's break down both parts of the question with detailed explanations:
1. Describe the set of numbers that are real numbers but cannot be expressed as one integer divided by another.
The set of numbers that are real but cannot be expressed as a fraction (one integer divided by another) falls into the category known as irrational numbers. Irrational numbers are real numbers that cannot be written as a simple fraction of two integers. They have decimal expansions that do not terminate or repeat. Examples include π (pi), √2 (the square root of 2), and the number e (Euler's number).
Answer: Irrational
2. To which sets of real numbers does zero belong?
Zero is a unique number with several important properties. It belongs to multiple sets of real numbers:
- Real Numbers: Zero is a real number as it can be placed on the number line.
- Rational Numbers: Zero is rational because it can be expressed as the fraction 0/1.
- Integer Numbers: Zero is an integer, as it is a whole number without a fractional part.
- Whole Numbers: Whole numbers include all non-negative integers, which start from zero and go to positive infinity. Hence, zero is included in this set.
Answer: Zero belongs to the sets of real, rational, integer, and whole numbers.
