List of mathematical symbols

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The following list contains some of the most notable symbols in mathematics. Please note that these symbols may have alternate meanings in different contexts.

These are symbols most commonly used in linear algebra
NameRead asDescriptionMeaningExample(s)
equalityequals, is equal toIf x=y, x and y represent the same value or thing.2+3=5
definitionis defined asIf x≡y, x is defined as another name of y(a+b)2≡a2+2ab+b2
approximately equalis approximately equal toIf x≈y, x and y are almost equal.√2≈1.41
inequationdoes not equal, is not equal toIf x≠y, x and y do not represent the same value or thing.1+1≠3
strict inequality
is less thanIf x<y, x is less than y.4<5
is greater thanIf x>y, x is greater than y.3>2
is much less thanIf x≪y, x is much less than y.1≪999999999
is much greater thanIf x≫y, x is much greater than y.999999999≫0.001
is less than or equal toIf x≤y, x is less than or equal to y.5≤6 and 5≤5
is greater than or equal toIf x≥y, x is greater than or equal to y.2≥1 and 2≥2
proportionalityis proportional toIf x∝y, then y=kx for some constant k.If y=4x then y∝x and x∝y
additionplusx+y is the sum of x and y.2+3=5
subtractionminusx-y is the subtraction of y from x5-3=2
multiplicationtimesx×y is the multiplication of x by y4×5=20
x·y is the multiplication of x by y4·5=20
divisiondivided byx÷y or x/y is the division of x by y20÷4=5 and 20/4=5
plus-minusplus or minusx±y means both x+y and x-yThe equation 3±√9 has two solutions, 0 and 6.
minus-plusminus or plus4±(3∓5) means both 4+(3-5) and 4-(3+5)6∓(1±3)=2 or 4
square rootsquare root√x is a nonnegative number whose square is x.√4=2
summationsum over … from … to … of, sigma is the same as x1+x2+x3+...+xn
multiplicationproduct over … from … to … of is the same as x1×x2×x3×....×xn=1×2×3×4×5=120
factorialfactorialn! is the product 1×2×3...×n5!=1×2×3×4×5=120
material implicationimpliesA⇒B means that if A is true, B must also be true, but if A is false, B is unknown.x=3⇒x2=9, but x2=9⇒x=3 is false, because x could also be -3.
material equivalenceif and only ifIf A is true, B is true and if A is false, B is false.x=y+1⇔x-1=y
absolute valueabsolute value of|x| is the distance along the real line (or across the complex plane) between x and zero|5|=5 and |-5|=5
parallelis parallel toIf A||B then A and B are parallel
perpendicularis perpendicular toIf A⊥B then A is perpendicular to B
congruenceis congruent toIf A≅B then shape A is congruent to shape B (has the same measurements)
golden ratiogolden ratioThe golden ratio is an irrational number equal to (1+√5)÷2 or approximately 1.6180339887.
infinityinfinity∞ is a symbol used to represent unending amounts.
set membershipis an element ofa∈S means that a is an element of the set S3.5∈ℝ, 1∈ℕ, 1+i∈ℂ
is not an element ofa∉S means that a is not an element of the set S2.1∉ℕ, 1+i∉ℝ
Set bracketsthe set of{a,b,c} is the set consisting of a, b, and cℕ={0,1,2,3,4,5...}
Natural numbersNℕ denotes the set of natural numbers {0,1,2,3,4,5...} (0 may or may not be included as natural number)
IntegersZℤ denotes the set of integers (-3,-2,-1,0,1,2,3...)
Rational numbersQℚ denotes the set of rational numbers (numbers that can be written as a fraction a/b where a∈ℤ, b∈ℕ)8.323∈ℚ, 7∈ℚ, π∉ℚ
Real numbersRℝ denotes the set of real numbersπ∈ℝ, 7∈ℝ, √(-1)∉ℝ
Complex numbersCℂ denotes the set of complex numbers√(-1)∈ℂ
Meanbar, overbarx̄ is the mean (average) of xiif x={1,2,3} then x̄=2
complex conjugatethe complex conjugate of xIf x=a + bi, then x̄=a - bi where i=√(-1)x=-4 + 5.3i, x̄=-4 - 5.3i
[+|-]situational plus minusEither plus or minus depending on the situation.If y=[+|-]x then x is either positive or negative depending on the situation.y=[+|-]x y equals either +x or -x depending on the scenario.

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