Describe all the sets and subsets the number 2/3 belongs to and enter the number corresponding to the correct answer as your response

1 answer

The number \( \frac{2}{3} \) belongs to several sets and subsets in mathematics. Here is the list:

  1. Rational Numbers (\( \mathbb{Q} \)): Since \( \frac{2}{3} \) can be expressed as a fraction of two integers (where the denominator is not zero), it is a rational number.
  2. Real Numbers (\( \mathbb{R} \)): All rational numbers are also real numbers.
  3. Numbers between 0 and 1: \( \frac{2}{3} \) falls between 0 and 1, thus belongs to the set of positive real numbers less than 1.
  4. Positive Numbers: \( \frac{2}{3} \) is a positive number.

Based on these classifications, we have:

  1. \( \mathbb{Q} \) (rational numbers)
  2. \( \mathbb{R} \) (real numbers)
  3. Positive rational numbers
  4. Real numbers between 0 and 1
  5. Positive numbers

If there is a specific numbering system or answer key you are referring to, please provide that, and I can help you find the exact number corresponding to the answer. In general mathematical contexts, we can conclude that \( \frac{2}{3} \) is part of the mentioned sets and subsets.