Mastering Algebra: A Visual Guide to Essential Symbols and Notations.
Symbol | Symbol Name | Meaning / definition | Example |
---|---|---|---|
x | x variable | unknown value to find | when 2 x = 4, then x = 2 |
= | equals sign | equality | 5 = 2+3 5 is equal to 2+3 |
≠ | not equal sign | inequality | 5 ≠ 4 5 is not equal to 4 |
≡ | 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! = 1*2*3*4 = 24 |
| x | | vertical bars | absolute value | | -5 | = 5 |
f ( x) | function of x | maps values of x to f(x) | f ( x) = 3 x+5 |
( f ∘ g) | function composition |
( f∘ g) ( x) = f ( g( x)) |
f ( x)=3 x, 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 = t _{ 1 }- t _{ 0 } |
∆ | discriminant | Δ = b ^{2} - 4 ac | |
∑ | sigma | summation - sum of all values in range of series | ∑ x _{i}= x _{1} +x _{2} +...+x _{ n } |
∑∑ | sigma | double summation | |
∏ | capital pi | product - product 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→∞ |
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 |
Symbol | Symbol Name | Meaning / definition | Example |
---|---|---|---|
· | dot | scalar product | a · b |
× | cross | vector product | a × b |
A⊗ B | tensor product | tensor product of A and B | A ⊗ B |
inner product | |||
[ ] | brackets | matrix of numbers | |
( ) | parentheses | matrix of numbers | |
| A | | determinant | determinant of matrix A | |
det( A) | determinant | determinant of matrix A | |
|| x || | double vertical bars | norm | |
A ^{ T } | transpose | matrix transpose | ( A ^{T}) _{ij} = ( A) _{ji} |
A ^{†} | Hermitian matrix | matrix conjugate transpose | ( A ^{†}) _{ij} = ( A ) _{ji} |
A ^{ * } | Hermitian matrix | matrix conjugate transpose | ( A ^{*}) _{ij} = ( A ) _{ji} |
A ^{ -1 } | inverse matrix | A A ^{-1} = I | |
rank( A) | matrix rank | rank of matrix A | rank( A) = 3 |
dim( U) | dimension | dimension of matrix A | dim( U) = 3 |
In algebra, the symbol 'x' is often used as a variable to represent an unknown quantity or a placeholder for a value that can vary. It plays a crucial role in solving equations and expressing relationships between quantities.