Question
Irrational numbers are real numbers
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GPT-4o mini
Yes, that is correct. Irrational numbers are indeed a subset of real numbers. Real numbers consist of both rational and irrational numbers.
Rational numbers are numbers that can be expressed as the quotient of two integers (where the denominator is not zero), such as \(\frac{1}{2}\) or \(-3\).
Irrational numbers, on the other hand, cannot be expressed as a simple fraction. They have non-repeating, non-terminating decimal expansions. Examples of irrational numbers include \( \pi \) (approximately 3.14159...) and the square root of 2 (\(\sqrt{2} \approx 1.41421...\)). These numbers fall within the category of real numbers, along with all rational numbers.
Rational numbers are numbers that can be expressed as the quotient of two integers (where the denominator is not zero), such as \(\frac{1}{2}\) or \(-3\).
Irrational numbers, on the other hand, cannot be expressed as a simple fraction. They have non-repeating, non-terminating decimal expansions. Examples of irrational numbers include \( \pi \) (approximately 3.14159...) and the square root of 2 (\(\sqrt{2} \approx 1.41421...\)). These numbers fall within the category of real numbers, along with all rational numbers.