Symbols for science

mathematical symbol

Symbol	Meaning / definition	Example
=	equality	5 = 2+3
≠	inequality	5 ≠ 4
>	greater than	5 > 4
<	less than	4 < 5
≥	greater than or equal to	5 ≥ 4
≤	less than or equal to	4 ≤ 5
( )	calculate expression inside first	2 × (3+5) = 16
[ ]	calculate expression inside first	[(1+2)*(1+5)] = 18
+	addition	1 + 1 = 2
−	subtraction	2 − 1 = 1
±	both plus and minus operations	3 ± 5 = 8 and -2
∓	both minus and plus operations	3 ∓ 5 = -2 and 8
*	multiplication	2 * 3 = 6
×	multiplication	2 × 3 = 6
∙	multiplication	2 ∙ 3 = 6
÷	division	6 ÷ 2 = 3
/	division	6 / 2 = 3
–	division / fraction
mod	remainder calculation	7 mod 2 = 1
.	decimal point, decimal separator	2.56 = 2+56/100
ab	exponent	23 = 8
a^b	exponent	2 ^ 3 = 8
√a	√a · √a  = a	√9 = ±3
3√a	3√a · 3√a  · 3√a  = a	3√8 = 2
4√a	4√a · 4√a  · 4√a  · 4√a  = a	4√16 = ±2
n√a		for n=3, n√8 = 2
%	1% = 1/100	10% × 30 = 3

Geometry symbols

Symbol	Meaning / definition	Example
∠	formed by two rays	∠ABC = 30º
∟	= 90º	α = 90º
º	1 turn = 360º degree	α = 60º
´	1º = 60´	α = 60º59'
´´	1´ = 60´´	α = 60º59'59''
AB	line from point A to point B
	line that start from point A
	arc from point A to point B	= 60º
|	perpendicular lines (90º angle)	AC | BC
||	parallel lines	AB || CD
≅	equivalence of geometric shapes and size	∆ABC ≅∆XYZ
~	same shapes, not same size	∆ABC ~∆XYZ
Δ	triangle shape	ΔABC ≅ΔBCD
|x-y|	distance between points x and y	| x-y | = 5
π	π = 3.141592654... is the ratio between the circumference and diameter of a circle
rad	radians angle unit	360º = 2π rad
grad	grads angle unit	360º = 400 grad

Symbol	Meaning / definition	Example
≡	identical to
≜	equal by definition
:=	equal by definition
~	weak approximation	11 ~ 10
≈	approximation	sin(0.01) ≈ 0.01
∝	proportional to	y ∝ x when y = kx, k constant
∞	infinity symbol
≪	much less than	1 ≪ 1000000
≫	much greater than	1000000 ≫ 1
( )	calculate expression inside first	2 * (3+5) = 16
[ ]	calculate expression inside first	[(1+2)*(1+5)] = 18
{ }	set
⌊x⌋	rounds number to lower integer	⌊4.3⌋= 4
⌈x⌉	rounds number to upper integer	⌈4.3⌉= 5
x!	factorial	4! = 1*2*3*4 = 24
| x |	absolute value	| -5 | = 5
f (x)	maps values of x to f(x)	f (x) = 3x+5
(f ∘g)	(f ∘g) (x) = f (g(x))	f (x)=3x, g(x)=x-1 ⇒(f ∘g)(x)=3(x-1)
(a,b)	(a,b) = {x | a < x < b}	x ∈ (2,6)
[a,b]	[a,b] = {x | a ≤ x ≤ b}	x ∈ [2,6]
∆	change / difference  dell	∆t = t1 - t0
∆	Δ = b2 - 4ac
∑	summation - sum of all values in range of series	∑ xi= x1+x2+...+xn
∑∑	double summation
∏	product - product of all values in range of series	∏ xi=x1∙x2∙...∙xn
e	e = 2.718281828...	e = lim (1+1/x)x , x→∞
γ	γ = 0.527721566...
φ	golden ratio constant
π	π = 3.141592654... is the ratio between the circumference and diameter of a circle	c = π·d = 2·π·r