Algebra Symbols

Algebra is a branch of mathematics that deals with symbols and the rules that govern their use. These symbols are known as variables in algebra because they represent quantities with no set values. Equations in mathematics explain relationships between variables in the same way that sentences indicate relationships between specific words. It is critical to understanding the important mathematical symbols and terminology used in algebra.

Algebraic Symbol	Name	Definition of the symbol	Example (if necessary)
x	x variable	unknown value to find	when 3 x = 6, then x = 2
:=	equal by definition	equal by definition
≈	approximately equal	approximation	sin (0.02) ≈ 0.02
∝	proportional to	proportional to	y ∝ x when y = ax, a constant
~	approximately equal	weak approximation	10.2 ~ 10
≜	equal by definition	equal by definition
[ ]	brackets	calculate expression inside first	[(1+3)*(1+4)] = 20
≫	much greater than	much greater than	500000 ≫ 1
( )	parentheses	calculate expression inside first	2 * (3+4) = 14
⌊ x ⌋	floor brackets	rounds number to lower integer	⌊3.2⌋= 3
∞	lemniscate	infinity symbol
≡	equivalence	identical to
\| x \|	single vertical bar	absolute value	\| -9 \| = 9
≪	much less than	much less than	1 ≪ 8000000
{ }	braces	set
⌈ x ⌉	ceiling brackets	rounds number to upper integer	⌈4.1⌉= 5
f ( x )	function of x	maps values of x to f(x)	f ( x ) = 7x +8
( f ∘ g )	function composition	( f ∘ g ) ( x ) = f ( g ( x ))	f ( x )=8 x , g ( x )= x-4 ⇒( f ∘ g )( x )=8( x -4)
( a , b )	open interval	( a , b ) = { x \| a < x < b }	x ∈ (1,5)
[ a , b ]	closed interval	[ a , b ] = { x \| a ≤ x ≤ b }	x ∈ [0,5]
∆	delta	change / difference	∆ t = t 1 – t 0
∑	sigma	summation – sum of all values in range of series	∑ x i = x 1 +x 2 +…+x n
e	e constant / Euler’s number	e = 2.718281828…	e = lim (1+1/ x) x, x → ∞
∆	discriminant	Δ = b 2 – 4 ac
∏	capital pi	product – product of all values in range of series	∏ x i =x 1 ∙x 2 ∙…∙x n
π	pi constant	π = 3.141592654… is the ratio between the circumference and diameter of a circle	c = π · d = 2· π · r
∑∑	sigma	double summation	∑ 2 j = 1 ∑ 8 i = 1 x i , j = ∑ 8 i = 1 x i , j + ∑ 8 i = 1 x i , 2
γ	Euler-Mascheroni constant	γ = 0.527721566…
φ	golden ratio	golden ratio constant
Symbol	Symbol Name	Meaning/definition	Example
A -1	inverse matrix	A A -1 = I
×	cross	vector product	a × b
⟨ x , y ⟩ <	inner product
rank( A )	matrix rank	rank of matrix A	rank( A ) = 4
∙	dot	scalar product	a ∙ b
det(A)	determinant	determinant of matrix A
[ ]	brackets	matrix of numbers
( )	parentheses	matrix of numbers
A ⊗ B	tensor product	tensor product of A and B	A ⊗ B

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Algebra Symbols

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