List of mathematical symbols

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Some Basic Mathematical Symbols[change | change source]

Please note that many of these symbols may have alternate meanings and may also differ from those used in computer science.

Symbol Name Read as Meaning Example
=
equality equals, is equal to If x=y, x and y represent the same value or thing. 2+3=5
definition is defined as If x≡y, x is defined as another name of y (a+b)2≡a2+2ab+b2
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. 1≪999999999
is much greater than If x≫y, x is much greater than y. 88979808≫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
×
multiplication times x×y is the multiplication of x by y 4×5=20
·
x·y is the multiplication of x by y 4·5=20
÷
division divided by x÷y or x/y is the division of x by y 20÷4=5 and 20/4=5
/
20/4=5
±
plus-minus plus or minus x±y means both x+y and x-y The equation 3±√9 has two solutions, 0 and 6.
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 number whose square is x. √4=2 or -2
summation sum over … from … to … of, sigma \sum_{k=1}^{n}{x_k} is the same as x1+x2+x3+xk \sum_{k=1}^{5}{k+2}=3+4+5+6+7=25
multiplication product over … from … to … of \prod_{k=1}^{n}{x_k} is the same as x1×x2×x3×xk \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 |5|=5 and |-5|=5
||
parallel is parallel to If A||B then A and B are parallel
perpendicular is perpendicular to If A⊥B then A is perpendicular to B
congruence is congruent to If A≅B then shape A is congruent to shape B (has the same measurements)
φ
golden ratio golden ratio The golden ratio is an irrational number equal to (1+√5)÷2 or approximately 1.6180339887.
infinity infinity ∞ is a number greater than every real number.
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 ℕ={0,1,2,3,4,5}
Natural numbers N ℕ denotes the set of natural numbers {0,1,2,3,4,5...}
Integers Z ℤ denotes the set of integers (-3,-2,-1,0,1,2,3...)
Rational numbers Q ℚ 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 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