For each set, list all elements that belong to the (a)...

For each set, list all elements that belong to the
(a) natural numbers
(b) whole numbers
(c) integers
(d) rational numbers
(e) irrational numbers
(f) real numbers
$$\left\{-\sqrt{100},-\frac{13}{6},-1,5.23,9 . \overline{14}, 3.14, \frac{22 {7}\right\}$$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Natural Numbers

Natural numbers are the set of positive whole numbers typically used for counting. They start from 1 and include numbers like 1, 2, 3, and so on. In some contexts, the set may include 0, but conventionally they begin from 1.

Whole Numbers

Whole numbers are non-negative integers that include 0 along with the natural numbers. They form a basic and fundamental set in mathematics used for counting and ordering.

Integers

Integers extend whole numbers by including the negatives of natural numbers. This set contains zero along with both positive and negative whole numbers, forming a complete set like ..., -3, -2, -1, 0, 1, 2, 3, ...

Rational Numbers

Rational numbers are those that can be expressed as the quotient of two integers, with a non-zero denominator. They include fractions and integers, and their decimal representations are either terminating or repeating.

Irrational Numbers

Irrational numbers cannot be expressed as a simple fraction of two integers. They have non-repeating, non-terminating decimal expansions and arise from certain roots or constants, filling the number line between rational numbers.

Real Numbers

Real numbers encompass all the numbers that can exist on the number line, including both rational and irrational numbers. This set represents all possible magnitudes along the continuum of numbers.

Transcript

Please give Ace some feedback