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Common mathematical symbols and terms: Mathematical glossary

Mathematical symbols and terminology can be confusing and can be an obstacle to learning and understanding basic mathematics.

This page complements our arithmetic skills page and provides a quick vocabulary of mathematical symbols and terminology common to concise definitions.

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Common Mathematical Symbols

+ Addition, Plus, Positive

The addition symbol + is usually used to indicate that two or more numbers should be added together, for example, 2 + 2.

The + symbol can also be used to indicate a positive number although this is less common, for example, +2. Our page on Positive and Negative Numbers explains that a number without a sign is considered to be positive, so the plus is not usually necessary.

− Subtraction, Minus, Negative

This symbol has two main uses in mathematics:

  1. − is used one or more numbers are to be subtracted, for example, 2 − 2.
  2. The − symbol is also commonly used to show a minus or negative number, such as −2.

× or * or . Multiplication

These symbols have the same meaning; commonly × is used to mean multiplication handwritten or used on a calculator 2 × 2, for example.

The symbol * is used in spreadsheets and other computer applications to indicate a multiplication, although * does have other more complex meanings in mathematics.

Less commonly, multiplication may also be symbolised by a dot . or indeed by no symbol at all. For example, if you see a number written outside brackets with no operator (symbol or sign), then it should be multiplied by the contents of the brackets: 2(3+2) is the same as 2×(3+2).

÷ or / Division

These symbols are both used to mean division in mathematics. ÷ is used commonly in handwritten calculations and on calculators, for example, 2 ÷ 2.

/ is used in spreadsheets and other computer applications.

= Equals

The = equals symbol is used to show that the values on either side of it are the same. It is most commonly used to show the result of a calculation, for example 2 + 2 = 4, or in equations, such as 2 + 3 = 10 − 5.

You may also come across other related symbols, although these are less common:

  •  means not equal. For example, 2 + 2 
  •  means identical to. This is similar to, but not exactly the same as, equals. Therefore, if in doubt, stick to =.
  •  means approximately equal to, or almost equal to. The two sides of a relationship indicated by this symbol will not be accurate enough to manipulate mathematically.

This symbol 

This symbol > means greater than, for example 4 > 2.

≤ ≥

≪ ≫ These symbols are less common and mean much less than, or much greater than.

± Plus or Minus

This symbol ± means ‘plus or minus'. It is used to indicate, for example, confidence intervals around a number.

The answer is said to be ‘plus or minus' another number, or in other words, within a range around the given answer.

For example, 5 ± 2 could in practice be any number from 3 to 7.

∑ Sum

The ∑ symbol means sum.

∑ is the Greek capital sigma character. It is used commonly in algebraic functions, and you may also notice it in Excel – the AutoSum button has a sigma as its icon.

° Degree

Degrees ° are used in several different ways.

  • As a measure of rotation – the angle between the sides of a shape or the rotation of a circle. A circle is 360° and a right angle is 90°. See our section on Geometry for more.
  • A measure of temperature. Degrees Celsius or Centigrade are used in most of the world (with the exception of the USA). Water freezes at 0°C and boils at 100°C. In the USA Fahrenheit is used. On the Fahrenheit scale water freezes at 32°F and boils at 212°F. See our page: Systems of Measurement for more information.

∠ Angle

The angle symbol ∠ is used as shorthand in geometry (the study of shapes) for describing an angle.

The expression ∠ABC is used to describe the angle at point B (between points A and C). Similarly, ∠BAC would be used to describe the angle of point A (between points B and C). For more on angles and other geometric terms see our pages on Geometry.

√ Square Root

√ is the symbol for square root. A square root is the number that, multiplied by itself, gives the original number.

For example, the square root of 4 is 2, because 2 x 2 = 4. The square root of 9 is 3, because 3 x 3 = 9.

n Power

A superscripted integer (any whole number n) is the symbol used for the power of a number.

For example,32, means 3 to the power of 2, which is the same as 3 squared (3 x 3).

43 means 4 to the power of 3 or 4 cubed, that is 4 × 4 × 4.

Powers are also used as a shorthand way to write large and small numbers.

Large numbers

106 is 1,000,000 (one million).

109 is 1,000,000,000 (one billion).

1012 is 1,000,000,000,000 (one trillion).

10100 written long-hand would be 1 with 100 0's (one Googol).

Small numbers

10-3 is 0.001 (one thousandth)

10-6 is 0.000001 (one millionth)

Powers can also be written using the ^ symbol.

10^6 = 106 = 1,000,000 (one million).

. Decimal Point

. is the decimal point symbol, often referred to simply as ‘point'. See our page on Decimals for examples of its use.

, Thousands Separator

A comma can be used to split large numbers and make them easier to read.

A thousand can be written as 1,000 as well as 1000 and a million as 1,000,000 or 1000000. The comma splits larger numbers into blocks of three digits.

In most English speaking countries the , does not have any mathematical function, it is simply used to make numbers easier to read.

In some other countries, especially in Europe, the comma may be used instead of a decimal point and indeed, a decimal point may be used in place of a comma as a visual separator.

[ ], ( ) Brackets, Parentheses

Brackets ( ) are used to determine the order of a calculation as dictated by the BODMAS rule.

Parts of a calculation included within brackets are calculated first, for example

  • 5 + 3 × 2 = 11
  • (5 + 3) × 2 = 16

% Percentage

The % symbol means percentage, or the number out of 100.

π Pi

π or Pi is the Greek character for the ‘p' sound. It occurs frequently in mathematics and is a mathematical constant. Pi is a circle's circumference divided by its diameter and has the value 3.141592653. It is an irrational number, which means that its decimal places continue to infinity.

∞ Infinity

The ∞ symbol signifies infinity, the concept that numbers go on for ever.

However large a number you have, you can always have a larger one, because you can always add one to it.

Infinity is not a number, but the idea of numbers going on for ever. You cannot add one to infinity, any more than you can add one to a person, or to love or hate.

x¯ (x-bar) Mean

x¯ is the mean of all the possible values of x.

You will mostly come across this symbol in statistics.

! Factorial

! is the symbol for factorial.

n! is the product (multiplication) of all the numbers from n down to 1, inclusive, i.e. n × (n−1) × (n−2) × … × 2 × 1.

For example:

5! = 5 × 4 × 3 × 2 × 1 = 120

10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 3,628,800

| Pipe

Pipe ‘|' is also also referred to as vertical bar, vbar, pike and has many uses in mathematics, physics and computing.

Most commonly in basic mathematics, it used to denote absolute value or modulus of a real number, where |x| is the absolute value or modulus of x.

Mathematically, this is defined as

Simply, |x| is the non-negative value of x. For example, the modulus of 6 is 6 and the modulus of −6 is also 6.

It is also used in probability, where P(Z|Y) denotes the probability of X given Y.

∝ Proportional

 means ‘is proportional to', and is used to show something that varies in relation to something else.

For example, if x = 2y, then x ∝ y.

∴ Therefore

∴ is a useful shorthand form of ‘therefore', used throughout maths and science.

∵ Because

∵ is a useful shorthand form of ‘because', not to be confused with ‘therefore'.


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