List the numbers in each set that are (a) Natural numbers,...

List the numbers in each set that are (a) Natural numbers, (b) Integers, (c) Rational numbers, (d) Irrational numbers, (e) Real numbers.
$C=\left\{0,1, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}\right\}$

Key Concepts

Real numbers

Real numbers encompass all the numbers that can be found on the number line. This set includes rational numbers, which can be expressed as fractions, as well as irrational numbers, which have non-repeating, non-terminating decimal expansions. Essentially, the real numbers represent all possible magnitudes of continuous quantities.

Irrational numbers

Irrational numbers are numbers that cannot be expressed as a simple fraction of two integers. Their decimal representations are non-repeating and non-terminating. They include numbers such as ? and ?2, and by definition, are not rational.

Integers

Integers include all whole numbers, both positive and negative, as well as zero. This set is denoted by {..., -3, -2, -1, 0, 1, 2, 3, ...}. Integers do not have fractional or decimal components, representing complete units without any parts.

Natural numbers

Natural numbers are the set of positive integers typically used for counting. They start from 1 and go upwards (1, 2, 3, …). Some definitions include 0 as a natural number, but in many contexts 0 is excluded. The exact definition depends on the mathematical context or convention being used.

Rational numbers

Rational numbers are numbers that can be expressed as a fraction where both the numerator and the denominator are integers and the denominator is non-zero. This set includes integers as they can be expressed as a fraction with a denominator of 1, as well as fractions and terminating or repeating decimals.

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