Mathematical Language and Symbols

Vocabulary flashcards covering core definitions and terms from Module 2 on Mathematical Language and Symbols.

Language

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

Precise

A characteristic of the language of mathematics that means able to make very fine distinctions.

Concise

A characteristic of the language of mathematics that means able to say things briefly.

Powerful

A characteristic of the language of mathematics that means able to express complex thoughts with relative ease.

Mathematical 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.

Set

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

Element

A member of a set, represented by the symbol $\in$ which is read as 'is an element of'.

Function

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

Relation

A mathematical object that refers to a potential relationship between objects, such as $=$ or $<$.

Logical Connective

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

Negation

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

Conjunction

A compound sentence formed by using the word 'and' to join two simple sentences, represented symbolically as $p \wedge q$ using the symbol $\wedge$.

Disjunction

A compound sentence formed by using the word 'or' to join two simple sentences, represented symbolically as $p \vee q$ using the symbol $\vee$.

Implication

A relationship between two statements where $p \Rightarrow q$ means that if $p$ is true, then $q$ must also be true.

Premise

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

Conclusion

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