Mathematical Language and Symbols

A set of vocabulary flashcards defining key concepts, terminology, characteristics, and symbols of mathematical language and elementary logic.

Language

A complex system of words and symbols, either spoken or written, used by a particular community as a means of communication.

Expression

The mathematical analog of an English noun; a correct arrangement of mathematical symbols used to represent a mathematical object of interest without stating a complete thought.

Mathematical Sentence

The mathematical analog of an English sentence; a correct arrangement of mathematical symbols that states a complete thought.

Precise

A characteristic of the language of mathematics describing the ability to make very fine distinctions.

Concise

A characteristic of the language of mathematics describing the ability to say things briefly.

Powerful

A characteristic of the language of mathematics describing the ability to express complex thoughts with relative ease.

Set

A collection of objects, which in mathematical discourse are mathematical objects such as numbers, points in space, or other sets.

Element

A member of a set, symbolized by $\in$ which is usually read as 'is an element of'.

Function

A mathematical transformation that takes a mathematical object and transforms it into another one.

Relation

A mathematical object or potential relationship that behaves like an adjectival phrase and refers to a property rather than an object, such as 'is less than' ($<$), 'equals' ($=$), or 'is an element of' ($\in$).

Logical Connective

A symbol or word used to connect two or more sentences, also called a logical operator, which can be expressed as a truth function.

Negation

The opposite of a statement, usually employing the word 'not', indicated by the symbol $\sim$.

Conjunction

A compound sentence formed by using the word 'and' to join two simple sentences, symbolized by $\land$ and expressed as $p \land q$.

Disjunction

A compound sentence formed by using the word 'or' to join two simple sentences, symbolized by $\lor$ and expressed as $p \lor q$.

Implication

A type of relationship between two statements where '$p \text{ implies } q$' ($p \Rightarrow q$) means that if $p$ is true, then $q$ must also be true.

Premise

The statement $p$ in an implication statement $p \Rightarrow q$.

Conclusion

The statement $q$ in an implication statement $p \Rightarrow q$.