Question
What number sets does the square root of 9 fit into?
Answers
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GPT-4o mini
The square root of 9 is 3. The number 3 fits into several number sets, including:
1. **Natural Numbers (ℕ)**: These are the positive integers starting from 1. Since 3 is a positive integer, it is a natural number.
2. **Whole Numbers (ℕ₀)**: Whole numbers include all natural numbers plus zero. Hence, 3 is also a whole number.
3. **Integers (ℤ)**: Integers include all whole numbers and their negative counterparts. Since 3 is a positive whole number, it is an integer.
4. **Rational Numbers (ℚ)**: Rational numbers are numbers that can be expressed as a fraction where both the numerator and the denominator are integers, and the denominator is not zero. The number 3 can be expressed as \( \frac{3}{1} \), so it is a rational number.
5. **Real Numbers (ℝ)**: Real numbers include all rational and irrational numbers. Since 3 is a rational number, it is also a real number.
6. **Complex Numbers (ℂ)**: Complex numbers are numbers that have a real part and an imaginary part. The number 3 can be expressed as \( 3 + 0i \), which means it is also a complex number.
In summary, the number 3 fits into the sets of natural numbers, whole numbers, integers, rational numbers, real numbers, and complex numbers.
1. **Natural Numbers (ℕ)**: These are the positive integers starting from 1. Since 3 is a positive integer, it is a natural number.
2. **Whole Numbers (ℕ₀)**: Whole numbers include all natural numbers plus zero. Hence, 3 is also a whole number.
3. **Integers (ℤ)**: Integers include all whole numbers and their negative counterparts. Since 3 is a positive whole number, it is an integer.
4. **Rational Numbers (ℚ)**: Rational numbers are numbers that can be expressed as a fraction where both the numerator and the denominator are integers, and the denominator is not zero. The number 3 can be expressed as \( \frac{3}{1} \), so it is a rational number.
5. **Real Numbers (ℝ)**: Real numbers include all rational and irrational numbers. Since 3 is a rational number, it is also a real number.
6. **Complex Numbers (ℂ)**: Complex numbers are numbers that have a real part and an imaginary part. The number 3 can be expressed as \( 3 + 0i \), which means it is also a complex number.
In summary, the number 3 fits into the sets of natural numbers, whole numbers, integers, rational numbers, real numbers, and complex numbers.