Mathematical Symbols: What They Mean and How to Use Them

What are mathematical symbols?

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

Using mathematical symbols makes it possible to record complex operations quickly and concisely, but they can only be read correctly if each individual symbol 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 that denote functions, for example. Symbols that require extensive specialist knowledge are generally used by experts in the field.

The most popular mathematical symbols, however, are those that represent important relationships and operations, mainly arithmetic symbols. Being able to interpret them is useful even for people outside the field of mathematics. The most commonly 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 the other mathematical operators. The minus symbol is also often represented by a hyphen (-).

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

The equals sign “=” is placed between elements that are equal to one another, 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 following it, for example, 6 < 7;
• the greater-than sign (>) indicates that the number or expression before it is larger than the one following 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, particularly 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 symbols that are used less frequently and are therefore less recognisable. 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, for example “2²”, read as two squared;
• 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.

We encounter these types of symbols primarily 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 interpreting many texts even easier.