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Commonly Used Symbols 

Commonly Used Symbols

Mathematical Composition

Stephen J. Lurie

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Commonly Used Symbols

Some commonly used symbols are as follows:




greater than

greater than or equal to


much greater than


less than

less than or equal to


much less than


plus or minus (This symbol should not be used to indicate variability around a central tendency (eg, “The control group had a mean [SD] value of 12 [7],” not “The control group had a mean of 12 ± 7.”)


integral from value of a to value of b


summation from a = 1 to a = 30


product of a = 1 to a = 30


delta (change, difference between values)



not equal to

approximately equal to

similar to (reserve for use in geometry and calculus; use words in other cases where “approximately” is meant)

congruent to

defined as



factorial, eg, n! = n(n − 1) (n − 2)… 1

The following symbols are usually reserved for specific values


pi (approximately 3.1416). Do not confuse with uppercase Π.


base of the system of natural logarithms (approximately 2.7183). See 21.4.3, Exponents, Logarithmic Expressions. In statistical equations, however, “e” may also represent the error term in a regression equation.


the square root of −1

For a list of additional symbols that are used in statistics, see 20.10, Study Design and Statistics, Statistical Symbols and Abbreviations.

The following are examples of these commonly used mathematical expressions:

>105 CFUs/mL


24.5 ± 0.5


L ≈ 2 × 1010 m

r ! (nr)!

f(x) = x + Δx

(ex + e−x)/2

y = dx/dt

Y = β1 + β2 + e

P < .001

kg · m · s−2


x+x22+x33+x44++xnn (note that in this case the operation sign is indicated on both sides of the ellipses)

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