GEC 14 - Chapter 2: Mathematical Language and Symbols

A complete list of vocabulary flashcards covering key definitions, characteristics, notation conventions, logic symbols, and set representations from Chapter 2.

Mathematical Language

The system used to communicate mathematical ideas, consisting of natural language using technical terms and grammatical conventions, supplemented by a highly specialized symbolic notation for mathematical formulas.

Precise

A characteristic of mathematical language that allows very fine distinctions or definitions among a set of mathematical symbols.

Concise

A characteristic of mathematical language where mathematicians can express lengthy expositions or sentences briefly.

Powerful

A characteristic of mathematical language where complex thoughts can be expressed with relative ease.

Mathematical Expression

A phrase in mathematics showing a combination of numbers, variables, and operation symbols without a comparison symbol; it does not make a statement and cannot be judged as true or false.

Mathematical Sentence

A complete thought in mathematics involving expressions connected by a relation symbol (such as $=$, $<$, or $>$) that can be judged as true or false.

PEMDAS / GEMDAS Rule

One of the most important conventions in mathematical language representing the order in which mathematical operations must be performed.

Notations

The standardized way of writing mathematical concepts.

Fixed Variables Convention

The mathematical convention of using the first part of the English alphabet (such as $a$, $b$, and $c$) as fixed variables.

Subscript and Superscript Variables Convention

The mathematical convention of using the middle part of the English alphabet as subscript and superscript variables.

Unknown Variables Convention

The mathematical convention of using the last part of the English alphabet (such as $x$, $y$, and $z$) as unknown variables.

Union Symbol ($\cup$)

A set theory symbol representing the union of set $A$ and set $B$ ($A \cup B$).

Intersection Symbol ($\cap$)

A set theory symbol representing the intersection of set $A$ and set $B$ ($A \cap B$).

Element Symbol ($\in$)

A set theory symbol indicating that an element belongs to a set ($x \in A$).

Subset Symbol ($\subset$)

A set theory symbol indicating that set $A$ is a subset of set $B$ ($A \subset B$).

Ellipses ($\dots$)

A notation indicating that there are still other items to follow in a set or sequence.

Conjunction Symbol ($\wedge$)

A logical symbol representing 'and' ($A \wedge B$).

Disjunction Symbol ($\vee$)

A logical symbol representing 'or' ($A \vee B$).

Negation Symbol ($\sim$)

A logical symbol representing 'not' ($\sim A$).

Implies Symbol ($\rightarrow$)

A logical symbol representing an if-then conditional statement ($A \rightarrow B$).

If and Only If Symbol ($\leftrightarrow$)

A logical symbol representing a biconditional statement ($A \leftrightarrow B$).

Universal Quantifier ($\forall$)

A logical symbol representing 'For all' ($\forall x$).

Existential Quantifier ($\exists$)

A logical symbol representing 'There exist' ($\exists x$).

Therefore Symbol ($\therefore$)

A logical symbol representing 'Therefore' ($\therefore C$).

Composition of Function Symbol ($\circ$)

A function operation symbol representing $f$ of $g$ of $x$ ($f \circ g(x)$).

Binary Operation Symbol ($*$)

A symbol representing a binary operation combining two values (e.g., $a * b = a + 17b$).

Set $N_0$

The natural numbers or whole numbers set with zero ($N_0 = \{0, 1, 2, 3, 4, \dots\}$).

Set $N_1$

The natural numbers or whole numbers set without zero ($N_1 = \{1, 2, 3, 4, 5, \dots\}$).

Set $Z$

The integer numbers set ($Z = \{\dots, -3, -2, -1, 0, 1, 2, 3, \dots\}$).

Set $Q$

The rational numbers set ($Q = \{x \mid x = a/b, a, b \in Z \text{ and } b \neq 0\}$).

Set $R$

The real numbers set ($R = \{x \mid -\infty < x < \infty\}$).

Set $C$

The complex numbers set ($C = \{z \mid z = a + bi, -\infty < a < \infty, -\infty < b < \infty\}$).