Mathematical Symbols: What They Mean and How to Use Them

What are mathematical symbols?

They are represented by symbols to which specific meanings are assigned in accordance with linguistic conventions.

Using mathematical symbols makes it possible to record complex operations quickly and concisely, but they can only be read correctly when each individual sign is interpreted properly.

The most commonly used mathematical symbols

There are several types of mathematical symbols used in everyday typography. These include symbols used in logic and mathematical analysis, as well as symbols for denoting functions. Signs that require extensive specialist knowledge are generally used by experts in the field.

The most popular mathematical symbols, however, are those representing important relationships and operations—primarily arithmetic symbols. Knowing how to interpret them is useful even for people outside the mathematical field. The most frequently used symbols of this kind include:

The plus (+) and minus (–) signs

These symbols are used, respectively, to indicate addition and subtraction, for example, 10 + 5 = 15 or 20 – 5 = 15. They have the same position and width as other mathematical operators. The minus symbol is also often represented by the hyphen (-).

Equality (=) and inequality (≠, <, >, ≤, ≥) signs

The equality symbol “=” is placed between elements that are equal, for example, 2 + 2 = 4. Inequality signs, on the other hand, are used to indicate that two elements are not equal, for example:

• the less-than sign (<) indicates that the number or expression before it is smaller than the one after it, for example, 6 < 7;
• the greater-than sign (>) indicates that the number or expression before it is greater than the one after it, for example, 7 > 6;
• the less-than-or-equal-to symbol (≤) means that the preceding element is less than or equal to the element that follows it, for example, 10 ≤ 11;
• the greater-than-or-equal-to symbol (≥) means that the preceding element is greater than or equal to the element that follows it, for example, 11 ≥ 11.

The multiplication (×) and division (÷) signs

The “×” and “÷” signs are used in texts to indicate multiplication and division, respectively—the main arithmetic operations. For example, 5 × 2 = 10 and 10 ÷ 2 = 5. Sometimes, especially in handwritten notation, the “÷” symbol is replaced by the simplified symbol “:” or the fraction bar “/”, while the “×” sign can also take the form of a dot “⋅”.

Other mathematical symbols

There are also many mathematical signs that are used less frequently and are therefore less familiar. These include symbols:

• used in mathematical logic, such as the “&” symbol, which denotes conjunction and is read as “and”;
• used in geometry and topology, such as “⟂”, which denotes perpendicularity;
• used in mathematical analysis, such as exponentiation notation, for example “2²”, read as two to the second power;
• used to denote sets and structures, such as “Z”, which denotes the set of integers;
• used to indicate specific functions, such as “cos”, the trigonometric cosine function.

You will encounter these types of symbols mainly in subject-specific texts, especially textbooks and academic articles. Nevertheless, it is worth being aware of their existence and distinguishing between individual symbols correctly. This makes many texts easier to interpret.