Im very confused on this.

List all the numbers from the given set that are: a. Natural numbers, b. Whole numbers, c. Integers, d. Rational numbers, e. Irrational numbers, f. Real numbers. {-3, -2/5, 0, 0.3, ✓3, 5.8, ✓100}
list all the natural numbers from the given set

Would 0 be the only one?

To determine the natural numbers from the given set, we need to understand what natural numbers are. Natural numbers are also known as counting numbers, which start from 1 and continue indefinitely. This means that natural numbers do not include negative numbers, decimals, or fractions.

Now, let's go through each number from the given set and determine if it is a natural number:

a. -3: Not a natural number since natural numbers do not include negative numbers.
b. -2/5: Not a natural number since natural numbers do not include fractions or decimals.
c. 0: Not a natural number since natural numbers do not include zero.
d. 0.3: Not a natural number since natural numbers do not include fractions or decimals.
e. ✓3: A natural number since it is a whole number greater than zero.
f. 5.8: Not a natural number since natural numbers do not include fractions or decimals.
g. ✓100: A natural number since it is a whole number greater than zero.

From the given set, the only natural numbers are ✓3 and ✓100.

To identify the numbers from the given set, let's go through each category step by step:

a. Natural numbers: Natural numbers are positive integers from 1 onwards. In this set, there are no natural numbers since all the numbers are either negative, fractions, or decimals. Therefore, the answer to "list all the natural numbers from the given set" is that there are none.

b. Whole numbers: Whole numbers include natural numbers as well as zero (0). In this set, the whole number is 0.

c. Integers: Integers include whole numbers as well as their negative counterparts. In this set, the integers are -3 and 0.

d. Rational numbers: Rational numbers include integers and any number that can be written as a fraction. In this set, the rational numbers are -3, -2/5, 0, 0.3, and √100 (since it simplifies to a whole number, which is a rational number).

e. Irrational numbers: Irrational numbers are numbers that cannot be expressed as a fraction or ratio. In this set, there are two irrational numbers: √3 and √100 (since it does not simplify to a fraction or a whole number).

f. Real numbers: Real numbers encompass all rational and irrational numbers. In this set, all the numbers listed are real numbers.

To clarify, the only number in the given set that is a natural number is 0.

Note: √100 = 10

I think they are after
a) {√100}
b) {0, √100}
c) {-3, 0, √100}
d) {-3, -2/5, 0, 0.3, 5.8, √100}
e) {√3}
f) all of them

If you were trying to pick the ones that were a,b,c,d,e and f, then 0 would not fit, because it is not irrational. In fact you should have recognized that NO number can be both rational and irrational!