Numbers and Their Properties

A set of vocabulary flashcards covering the properties and classifications of numbers as discussed in the lecture.

Real Numbers

Numbers that can be expressed as an infinite decimal expansion, including integers, rationals, and irrationals.

Irrational Numbers

Real numbers that cannot be written as a ratio of two integers; they do not terminate or repeat.

Rational Numbers

Real numbers that can be represented as a ratio of two integers, where the denominator is not zero.

Integers

Rational numbers that can be written without a fractional or decimal component.

Prime Numbers

Numbers greater than 1 that are divisible only by 1 and themselves.

Prime Factorization

The expression of a number as a product of its prime factors.

GCF (Greatest Common Factor)

The product of prime factors that are common across the numbers.

LCM (Least Common Multiple)

The smallest multiple that is common amongst a set of numbers.

Complex Numbers

Numbers composed of a real part and an imaginary part, expressed as a + bi.

Imaginary Numbers

Non-real numbers that give a negative result when squared.

Adding Complex Numbers

Add the real parts and the imaginary parts separately.

Multiplying Complex Numbers

Distribute and combine like terms, then substitute for any imaginary components.

Dividing Complex Numbers

Multiply by the conjugate to eliminate the imaginary unit from the denominator.