Mathematical Conventions and Concepts

A set of flashcards covering standard mathematical conventions and the four basic concepts of mathematics including sets, relations, functions, and binary operations.

Mathematical Convention

Standardized rules, notations, and procedures agreed upon worldwide for solving and writing math problems consistently.

Order of Operations (PEMDAS)

The agreed order for evaluating mathematical expressions: Parentheses, Exponents, Multiplication & Division, Addition & Subtraction.

Notation for Sets

The use of curly brackets ${1, 2, 3}$ to enclose distinct elements of a set.

Notation for Functions

Represented as $f(x)$, where $f$ names the function and $x$ is the independent variable.

Notation for Derivatives

Uses $\frac{d}{dx}$ or prime notation $f'(x)$ for derivatives.

Notation for Integrals

Uses $\int$ for integrals.

Notation for Series

Uses summation $\sum$ for series.

Notation for Sequences

Uses subscripted variables $a_n$ for terms in a sequence.

Sets

A well-defined collection of distinct objects or elements enclosed in curly braces $\{\}$.

Infinite Set

A set with an endless number of elements that continues indefinitely without stopping.

Finite Set

A set containing a countable, limited number of elements.

Ellipsis (…)

Indicates continuous continuation of a pattern.

Empty Set

A set containing no elements, denoted by $\emptyset$ or $\{\}$.

Subset

A set where all of its elements are entirely contained within another set.

Relations

A set of ordered pairs representing a relationship between two sets of values.

Domain (D)

The set of all first components ($x$-values) in ordered pairs.

Range (R)

The set of all second components ($y$-values) in ordered pairs.

Functions

A special type of relation where each element in the domain corresponds to exactly one element in the range.

Binary Operations

A rule for combining two elements to produce another element, such as addition, subtraction, multiplication, or division.