Let's evaluate each statement one by one:
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Every rational number is a natural number: False. Rational numbers include integers, fractions, and decimals that can be expressed as a ratio of two integers. Natural numbers are the positive integers (1, 2, 3, ...), and not all rational numbers fall into this category (e.g., \( \frac{1}{2} \) is rational but not a natural number).
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Every natural number is also an integer: True. Natural numbers (1, 2, 3, ...) are part of the set of integers (which also include 0 and negative integers).
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Every irrational number is also an integer: False. Irrational numbers cannot be expressed as a ratio of two integers and therefore are not integers. For example, \( \sqrt{2} \) and \( \pi \) are irrational numbers, but they are not integers.
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0.128128128... is an irrational number: False. The number 0.128128128... is a repeating decimal, which can be expressed as a fraction (specifically, \( \frac{128}{999} \)). Therefore, it is a rational number, not an irrational number.
In summary:
- False
- True
- False
- False
3 answers