List of mathematical symbols

meanings of symbols used in mathematics

The list below has some of the most common symbols in mathematics. However, these symbols can have other meanings in different contexts other than math.


SymbolNameRead asMeaningExample(s)
=
Equalis equal toIf x=y, x and y represent the same value or thing.5(2)=10
Definitionis defined asIf x≡y, x is defined as another name of yϕ≡(√5+1)/2≈1.618
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.0.001≪999999999
is much greater thanIf x≫y, x is much greater than y.999999999≫0.001
Inequality
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
× or ·
Multiplicationtimes

or multiplied by

x×y or x·y is the multiplication of x by y4×5=20 or 4·5=20
÷ or /
Divisiondivided byx÷y or x/y is the division of x by y20÷4=5 or 20/4=5
±
Plus-minusplus or minusx±y means both x+y and x-y1±2 represents both 3 and -1
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
Productproduct 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.|x|=x and |-x|=x
||
Parallelis parallel toIf A||B then line A will never touch line B, thus both lines are rotated in the same angle.x||(x+1)
Perpendicularis perpendicular toIf A⊥B then line A is touching line B in a 90 degrees angle.x⊥y
Congruenceis congruent toIf A≅B then shape A and B same shape and size, or A has the same shape and size as the mirror image of B.If two triangles, △ABC and △DEF, are congruent, it can be denoted as △ABC≅△DEF
φ
Golden ratiogolden ratioThe golden ratio is an irrational number equal to (1+√5)÷2 or approximately 1.6180339887.φ ≈ 1.6180339887
Infinityinfinity∞ is a symbol used to represent unending amounts.∞ + x = ∞
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 cS = { a, b, c }
Natural numbersNℕ denotes the set of natural numbers1∈ℕ, 2∈ℕ, 100∈ℕ
IntegersZℤ denotes the set of integers-1∈ℤ, 0∈ℤ, 30∈ℤ
Rational numbersQℚ denotes the set of rational numbers8.323∈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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