Introduction to Real Numbers

Vocabulary flashcards covering the basic classification, types of decimals, and inclusion relationships of real numbers.

Natural Numbers ($\mathbb{N}$)

The set of numbers $0, 1, 2, 3, 4, 5, \dots$ used primarily for counting objects.

Integers ($\mathbb{Z}$)

The set of whole positive and negative numbers and zero ($\dots, -5, -4, -3, -2, -1, 0, 1, 2, 3, \dots$), used to represent situations such as debts and temperatures.

Rational Numbers ($\mathbb{Q}$)

Numbers used to represent division or sharing of quantities, which can be expressed as fractions or decimals.

Exact Decimal

A rational decimal number that has a finite number of digits, such as $0.25$.

Pure Periodic Decimal

A rational decimal number in which the repeating pattern of digits begins immediately after the decimal point, such as $2.1111\dots$ or $3.232323\dots$.

Mixed Periodic Decimal

A rational decimal number that contains one or more non-repeating digits right after the decimal point before the repeating pattern starts, such as $2.57333\dots$ or $5.12222\dots$.

Irrational Numbers ($\mathbb{I}$)

Numbers with infinite non-repeating decimal digits that cannot be expressed as a fraction, such as $\sqrt{2} \approx 1,97\dots$.

Real Numbers ($\mathbb{R}$)

The complete set of numbers used primarily for counting and ordering, combining all rational and irrational numbers.

Inclusion Relation

The structural containment relationship of number sets expressed as $\mathbb{N} \subset \mathbb{Z} \subset \mathbb{Q} \subset \mathbb{R}$, where irrational numbers belong to real numbers but not rational numbers ($\mathbb{I} \subset \mathbb{R}$).