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.