Mathematical Language and Symbols

Language

A complex system of words and symbols, spoken or written, used by a community for communication.

Language of Mathematics

A system that uses numbers and symbols with specific rules to express mathematical ideas and relationships.

Mathematical Symbols

Special signs used in mathematics to represent operations, relationships, or concepts.

Addition (+)

A mathematical operation used to combine numbers.

Subtraction (−)

A mathematical operation used to find the difference between numbers.

Multiplication (×)

A mathematical operation used to represent repeated addition.

Division (÷ or /)

A mathematical operation used to split a number into equal parts.

Grouping Symbols

Symbols such as ( ), [ ], and { } used to group numbers or expressions.

Set Symbols { }

Symbols used to show a collection of objects.

Pi (π)

A mathematical constant representing the ratio of a circle’s circumference to its diameter.

Infinity (∞)

A concept representing something that has no end.

Equals (=)

A symbol showing that two expressions have the same value.

Approximately Equal (≈)

A symbol indicating that two values are close but not exactly equal.

Not Equal (≠)

A symbol showing that two values are different.

Less Than (<)

A symbol showing that one value is smaller than another.

Greater Than (>)

A symbol showing that one value is larger than another.

Square Root (√)

A mathematical operation that finds a number which, when multiplied by itself, gives the original number.

Degree (°)

A unit used to measure angles or temperature.

Therefore (∴)

A symbol meaning “as a result” or “it follows that”.

Precise (Mathematical Language)

The ability of mathematics to make exact and clear distinctions.

Concise (Mathematical Language)

The ability of mathematics to express ideas briefly.

Powerful (Mathematical Language)

The ability of mathematics to express complex ideas efficiently.

Expression

A correct arrangement of mathematical symbols that names a mathematical object and does not state a complete thought.

Mathematical Sentence

A correct arrangement of mathematical symbols that states a complete thought and can be true or false.

Truth Value

The classification of a mathematical sentence as true, false, or sometimes true/sometimes false.

Set

A collection of mathematical objects such as numbers or points.

Element

An object that belongs to a set.

Element Of (∈)

A symbol meaning “is an element of” or “belongs to a set”.

Function

A mathematical transformation that takes an input and produces an output.

Relation

A mathematical concept that describes a relationship between objects, such as equals or less than.

Logical Connective (Logical Operator)

A symbol or word used to connect two or more mathematical sentences.

Negation (~)

A logical operation that expresses the opposite of a statement.

Conjunction (∧)

A logical connective meaning “and” that joins two statements.

Disjunction (∨)

A logical connective meaning “or” that joins two statements.

Implication (⇒)

A logical relationship meaning “if p, then q”.

Premise

The first statement in an implication.

Conclusion

The statement that follows from the premise in an implication.