QuestionDetermine the group of sets for the number . Options: A. real, rational B. real, irrational C. real, rational, natural D. rational, natural, integers E. irrational, natural.
Studdy Solution
STEP 1
Assumptions1. The given number is
STEP 2
First, we need to understand the definitions of the different types of numbers.
- Real numbers This is the set of all numbers that can be expressed as a decimal or fraction, including both rational and irrational numbers.
- Rational numbers This is the set of all numbers that can be expressed as a fraction , where and are integers and .
- Irrational numbers This is the set of all numbers that cannot be expressed as a fraction. These numbers have decimal expansions that neither terminate nor become periodic.
- Natural numbers This is the set of all positive integers, starting from1.
- Integers This is the set of all whole numbers, including both positive and negative numbers, as well as zero.
STEP 3
Now, let's determine to which sets the number belongs.
First, we see that can be expressed as a fraction, so it is a rational number.
STEP 4
Next, since all rational numbers are also real numbers, is a real number.
STEP 5
However, is not a natural number, since natural numbers are positive integers and is neither positive nor an integer.
STEP 6
Also, is not an integer, since integers are whole numbers and is not a whole number.
STEP 7
Finally, is not an irrational number, since irrational numbers cannot be expressed as fractions and can be expressed as a fraction.
So, the number belongs to the sets of real numbers and rational numbers.
Therefore, the correct answer is A. real numbers, rational numbers.
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