Patterns, Sets, and Functions

Comprehensive vocabulary flashcards covering mathematical patterns, set operations and classifications, and functions based on the provided lecture notes.

Pattern

A repeated numerical, natural, shape, or daily life arrangement or structure.

Fibonacci Sequence

A sequence of numbers where each number is the sum of the $2$ previous numbers, such as $0, 1, 1, 2, 3, 5, 8$.

Bilateral Symmetry

A type of symmetry in which the left and right sides are balanced and identical.

Radial Symmetry

A type of symmetry where parts are arranged around the center, such as in plants, flowers, and starfish.

Fractals

Repeating patterns that appear at various scales in nature and mathematics.

Set

A collection of distinct objects grouped together, whose individual components are called elements or members.

Roster Method

A method of describing a set where elements are listed one by one inside brackets.

Set Builder Method

A method of describing a set using a rule and condition for its members, such as $A = \{x \mid x \text{ is a whole number less than } 6\}$.

Empty Set

A set that has $0$ elements, also called a null set, denoted by $\emptyset$ or $\{\}$.

Finite Set

A set containing an exact or countable group of elements.

Infinite Set

A set containing unlimited elements, represented with ellipses such as $\{1, 2, 3, 4, 5, \dots\}$.

Equal Sets

Sets that contain exactly the same elements, such as $A = \{1, 2, 3\}$ and $B = \{3, 2, 1\}$.

Equivalent Sets

Sets that contain the same number of members or share the same cardinality.

Universal Set

A set containing all the elements related to a particular subject, represented by $U$.

Disjoint Sets

Sets that have no common elements.

Subset

A set where all of its elements are also members of another set, denoted by $\subset$ or $\subseteq$.

Power Set

The set containing all possible subsets of a given set, written as $P(A)$.

Unequal Sets

Sets that contain at least one different element.

Overlapping Sets

Sets that share at least one common element.

Cardinality

The total number of elements contained within a set.

Venn Diagram

Visual representations using circles that show relationships between sets, created by John Venn.

Union of Sets

An operation that combines all elements from two sets, symbolized by $\cup$.

Intersection of Sets

An operation that finds the common elements shared between sets, symbolized by $\cap$.

Function

A special type of relation where each input in the domain is paired with only one output in the range.

Function Notation

The standard algebraic representation $f(x)$, read as "f of x".

Arrow Diagram

A mapping diagram used to show a relation or function by connecting inputs ($X$) to outputs ($Y$).