Zero belongs to several important sets of real numbers, including:
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The set of integers (ℤ): This set includes all whole numbers, both positive and negative, as well as zero.
- Example: {..., -2, -1, 0, 1, 2, ...}
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The set of rational numbers (ℚ): This set includes all numbers that can be expressed as the quotient of two integers, where the denominator is not zero. Zero can be expressed as \(0/1\) or \(0/n\) (for any non-zero integer \(n\)).
- Example: {..., -2, -1, 0, 1, 2, ...} (with fractions)
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The set of real numbers (ℝ): This includes all rational and irrational numbers. Since zero is a rational number, it is included in the set of real numbers.
- Example: All numbers on the number line, including whole numbers, fractions, and irrational numbers like \(\sqrt{2}\).
In conclusion, zero belongs to the integers, rational numbers, and real numbers.