# 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.

Symbol Name Read as Meaning Example(s)
=
Equal is equal to If x=y, x and y represent the same value or thing. 5(2)=10
Definition is defined as If x≡y, x is defined as another name of y ϕ≡(√5+1)/2≈1.618
Approximately equal is approximately equal to If x≈y, x and y are almost equal. √2≈1.41
Inequation does not equal, is not equal to If x≠y, x and y do not represent the same value or thing. 1+1≠3
<
Strict inequality
is less than If x<y, x is less than y. 4<5
>
is greater than If x>y, x is greater than y. 3>2
is much less than If x≪y, x is much less than y. 0.001≪999999999
is much greater than If x≫y, x is much greater than y. 999999999≫0.001
Inequality
is less than or equal to If x≤y, x is less than or equal to y. 5≤6 and 5≤5
is greater than or equal to If x≥y, x is greater than or equal to y. 2≥1 and 2≥2
Proportionality is proportional to If x∝y, then y=kx for some constant k. If y=4x then y∝x and x∝y
+
Addition plus x+y is the sum of x and y. 2+3=5
-
Subtraction minus x-y is the subtraction of y from x 5-3=2
× or ·
Multiplication times

or multiplied by

x×y or x·y is the multiplication of x by y 4×5=20 or 4·5=20
÷ or /
Division divided by x÷y or x/y is the division of x by y 20÷4=5 or 20/4=5
±
Plus-minus plus or minus x±y means both x+y and x-y 1±2 represents both 3 and -1
Minus-plus minus or plus 4±(3∓5) means both 4+(3-5) and 4-(3+5) 6∓(1±3)=2 or 4
Square root square root √x is a nonnegative number whose square is x. √4=2
Summation sum over … from … to … of, sigma ${\displaystyle \sum _{k=1}^{n}{x_{k}}}$ is the same as x1+x2+x3+...+xn ${\displaystyle \sum _{k=1}^{5}{(k+2)}=3+4+5+6+7=25}$
Product product over … from … to … of ${\displaystyle \prod _{k=1}^{n}{x_{k}}}$ is the same as x1×x2×x3×....×xn ${\displaystyle \prod _{k=1}^{5}{k}}$=1×2×3×4×5=120
!
Factorial factorial n! is the product 1×2×3...×n 5!=1×2×3×4×5=120
Material implication implies A⇒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 equivalence if and only if If A is true, B is true and if A is false, B is false. x=y+1⇔x-1=y
|…|
Absolute value absolute value of |x| is the distance along the real line (or across the complex plane) between x and zero. |x|=x and |-x|=x
||
Parallel is parallel to If A||B then line A will never touch line B, thus both lines are rotated in the same angle. x||(x+1)
Perpendicular is perpendicular to If A⊥B then line A is touching line B in a 90 degrees angle. x⊥y
Congruence is congruent to If 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 ratio golden ratio The golden ratio is an irrational number equal to (1+√5)÷2 or approximately 1.6180339887. φ ≈ 1.6180339887
Infinity infinity ∞ is a symbol used to represent unending amounts. ∞ + x = ∞
Set membership is an element of a∈S means that a is an element of the set S 3.5∈ℝ, 1∈ℕ, 1+i∈ℂ
is not an element of a∉S means that a is not an element of the set S 2.1∉ℕ, 1+i∉ℝ
{,}
Set brackets the set of {a,b,c} is the set consisting of a, b, and c S = { a, b, c }
Natural numbers N ℕ denotes the set of natural numbers 1∈ℕ, 2∈ℕ, 100∈ℕ
Integers Z ℤ denotes the set of integers -1∈ℤ, 0∈ℤ, 30∈ℤ
Rational numbers Q ℚ denotes the set of rational numbers 8.323∈ℚ, 7∈ℚ, π∉ℚ
Real numbers R ℝ denotes the set of real numbers π∈ℝ, 7∈ℝ, √(-1)∉ℝ
Complex numbers C ℂ denotes the set of complex numbers √(-1)∈ℂ
Mean bar, overbar x̄ is the mean (average) of xi if x={1,2,3} then x̄=2
Complex conjugate the complex conjugate of x If x=a ± bi, then x̄=a ∓ bi where i=√(-1) x=-4 + 5.3i, x̄=-4 - 5.3i
[+|-] Situational plus minus Either 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.