Question
Every Rational number is a Natural number. T or F?
Every natural number is also an integer. T or F?
Every Irrational number is also an Integer. T or F?
0.128128128… is an Irrational number. T or F?
Every natural number is also an integer. T or F?
Every Irrational number is also an Integer. T or F?
0.128128128… is an Irrational number. T or F?
Answers
GPT-4o mini
Let's analyze each statement one by one.
1. **Every Rational number is a Natural number.**
**False.** A rational number can be expressed as the ratio of two integers (e.g., \( \frac{1}{2} \)), but not all rational numbers are natural numbers (which are positive integers like 1, 2, 3, ...).
2. **Every natural number is also an integer.**
**True.** Natural numbers (0 or the set of positive integers) are a subset of integers. Therefore, every natural number is indeed an integer.
3. **Every Irrational number is also an Integer.**
**False.** Irrational numbers cannot be expressed as a fraction of two integers, such as \( \sqrt{2} \) or \( \pi \). Since integers are whole numbers (positive, negative, or zero) and rational numbers, irrational numbers cannot be integers.
4. **0.128128128… is an Irrational number.**
**False.** The number 0.128128128… is a repeating decimal, which means it can be expressed as a fraction (in this case, \( \frac{128}{990} \)). Therefore, it is a rational number, not an irrational number.
So the final answers are:
1. **False**
2. **True**
3. **False**
4. **False**
1. **Every Rational number is a Natural number.**
**False.** A rational number can be expressed as the ratio of two integers (e.g., \( \frac{1}{2} \)), but not all rational numbers are natural numbers (which are positive integers like 1, 2, 3, ...).
2. **Every natural number is also an integer.**
**True.** Natural numbers (0 or the set of positive integers) are a subset of integers. Therefore, every natural number is indeed an integer.
3. **Every Irrational number is also an Integer.**
**False.** Irrational numbers cannot be expressed as a fraction of two integers, such as \( \sqrt{2} \) or \( \pi \). Since integers are whole numbers (positive, negative, or zero) and rational numbers, irrational numbers cannot be integers.
4. **0.128128128… is an Irrational number.**
**False.** The number 0.128128128… is a repeating decimal, which means it can be expressed as a fraction (in this case, \( \frac{128}{990} \)). Therefore, it is a rational number, not an irrational number.
So the final answers are:
1. **False**
2. **True**
3. **False**
4. **False**