Number Systems

Flashcards covering key terms and definitions related to number systems.

Real Numbers

Collection of all rational and irrational numbers.

Rational Numbers

Numbers that can be expressed in the form of p/q, where p and q are integers and q≠0.

Irrational Numbers

Numbers that cannot be expressed in the form p/q, where p and q are integers.

Natural Numbers

The set of positive integers: N = {1, 2, 3, 4, …}

Whole Numbers

The set of non-negative integers: W = {0, 1, 2, 3, 4, …}

Integers

The set of whole numbers and their negative counterparts: Z = {…, -3, -2, -1, 0, 1, 2, 3, …}.

Prime Numbers

Natural numbers greater than 1 with exactly two distinct factors: 1 and the number itself.

Composite Numbers

Natural numbers greater than 1 that have more than two distinct factors.

Co-prime Numbers

Pairs of numbers that have no common factors other than 1.

Nth Root

The value that, when raised to the nth power, gives the original number.

Rationalization

The process of eliminating a radical in the denominator of a fraction.

Law of Exponents

Rules that describe how to handle exponents in mathematical expressions.

Infinite Rational Numbers

There are infinitely many rational numbers between any two given rational numbers.

Unique Representation on the Number Line

Every real number corresponds to exactly one point on the number line.

Representation of √2

An example of an irrational number on the number line.

Existence of Non-Rational Numbers

Irrational numbers like √2, √3 that cannot be expressed as fractions.

Operations on Real Numbers

Mathematical functions applied to real numbers, including addition, subtraction, multiplication, and division.

Terminating Decimal

A decimal that has a finite number of digits after the decimal point.

Recurring Decimal

A decimal that has digits that repeat infinitely.