Algebra symbols
| Symbol | Symbol Name | Meaning/Definition | Example |
|---|---|---|---|
| \( x \) | x variable | unknown value to find | \( \text{when} \ 2x = 4, \ \text{then} \ x = 2 \) |
| \( ≡ \) | equivalence | identical to | \( \) |
| \( \triangleq \) | 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 | \( \) |
| \( \lfloor x\rfloor \) | floor brackets | rounds number to lower integer | \( \lfloor 4.3 \rfloor = 4 \) |
| \( \lceil x \rceil \) | ceiling brackets | rounds number to upper integer | \( \lceil 4.3 \rceil =5 \) |
| \( x! \) | 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) | \( f (x) = 3x+5 \) |
| \( (f \circ g) \) | function composition | \( (f \circ g) (x) = f (g(x)) \) | \( f (x)=3x,g(x)=x-1 ⇒(f \circ g)(x)=3(x-1) \) |
| \( (a,b) \) | 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 = b2 - 4ac | \( \) |
| \( ∑ \) | summation - sum of all values in range of series | \( ∑ x_i= x_1+x_2+\cdots+x_n \) | |
| \( ∑∑ \) | sigma | double summation | \( \sum_{j=1}^2 \sum_{i=1}^8 x_{i,j} \) |
| \( ∏ \) | capital pi | product - product of all values in range of series | \( ∏ x_i=x_1\cdot x_2\cdot...\cdot x_n \) |
| \( e \) | 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 | \( c = πd = 2πr \) |
