To which sets of real numbers does zero belong to
Zero belongs to the set of real numbers (ℝ).
Zero belongs to several sets of real numbers. Here are a few sets that include zero:
1. Natural Numbers (ℕ): Zero does not belong to the set of natural numbers, as it consists of positive integers starting from 1.
2. Whole Numbers (ℤ̅): Zero belongs to the set of whole numbers, which includes all positive integers (1, 2, 3, ...) and zero (0).
3. Integers (ℤ): Zero belongs to the set of integers, which includes all whole numbers (0, ±1, ±2, ±3, ...).
4. Rational Numbers (ℚ): Zero belongs to the set of rational numbers, which are numbers that can be expressed as a fraction of two integers (e.g., 1/2, -3/4, 0/1).
5. Real Numbers (ℝ): Zero belongs to the set of real numbers, which includes all rational and irrational numbers. It represents the origin on the real number line.
In conclusion, zero belongs to the sets of whole numbers, integers, rational numbers, and real numbers.