Algebra sign and symbols

Details: Category: Mathematics notes and reviews

Algebra symbols

Symbol	Symbol Name	Meaning / definition	Example
x	x variable	unknown value to find	when 2x = 4, then x = 2
≡	equivalence	identical to
≜	equal by definition	equal by definition
:=	equal by definition	equal by definition
~	approximately equal	weak approximation	11 ~ 10
≈	approximately equal	approximation	sin(0.01) ≈ 0.01
∝	proportional to	proportional to	y ∝ x when y = kx, k constant
∞	lemniscate	infinity symbol
≪	much less than	much less than	1 ≪ 1000000
≫	much greater than	much greater than	1000000 ≫ 1
( )	parentheses	calculate expression inside first	2 * (3+5) = 16
[ ]	brackets	calculate expression inside first	[(1+2)*(1+5)] = 18
{ }	braces	set
⌊x⌋	floor brackets	rounds number to lower integer	⌊4.3⌋ = 4
⌈x⌉	ceiling brackets	rounds number to upper integer	⌈4.3⌉ = 5
x!	exclamation mark	factorial	4! = 123*4 = 24
\| x \|	vertical bars	absolute value	\| -5 \| = 5
f (x)	function of x	maps values of x to f(x)	f (x) = 3x+5
(f ∘ g)	function composition	(f ∘ g) (x) = f (g(x))	f (x)=3x,g(x)=x-1 ⇒(f ∘ g)(x)=3(x-1)
(a,b)	open interval	(a,b) = {x \| a < x < b}	x∈ (2,6)
[a,b]	closed interval	[a,b] = {x \| a ≤ x ≤ b}	x ∈ [2,6]
∆	delta	change / difference	∆t = t₁- t₀
∆	discriminant	Δ = b² - 4ac
∑	sigma	summation - sum of all values in range of series	∑ x_i= x₁+x₂+...+x_n
∑∑	sigma	double summation
∏	capital pi	product - product of all values in range of series	∏ x_i=x₁∙x₂∙...∙x_n
e	e constant / Euler's number	e = 2.718281828...	e = lim (1+1/x)^x , x→∞
γ	Euler-Mascheroni constant	γ = 0.5772156649...
φ	golden ratio	golden ratio constant
π	pi constant	π = 3.141592654... is the ratio between the circumference and diameter of a circle	c = π⋅d = 2⋅π⋅r