Symbols in Algebra
Common Symbols Used in Algebra
Symbols save time and space when writing. Here are the most common algebraic symbols (also see Symbols in Geometry):
| Symbol | Meaning | Example |
|---|---|---|
| + | add | 3+7 = 10 |
| − | subtract | 5−2 = 3 |
| × | multiply | 4×3 = 12 |
| · | multiply (as "×" can look like "x") | 4·3 = 12 |
| (none) | multiply side-by-side (the "hidden" multiply) | 4z = 4 × z |
| / | divide | 20/5 = 4 |
| ÷ | divide | 20÷5 = 4 |
| ( ) | grouping symbols (round brackets) | 2(a−3) |
| [ ] | grouping symbols (square brackets) | 2[ a−3(b+c) ] |
| { } | set symbols (curly brackets) | {1,2,3} |
| = | equals | 1+1 = 2 |
| ≈ | approximately equal to | π ≈ 3.14 |
| ≠ | not equal to | π ≠ 2 |
| < ≤ | less than, less than or equal to | 2 < 3 |
| > ≥ | greater than, greater than or equal to | 5 > 1 |
| ≡ | equivalent to (identical in value or meaning) | |
| ∝ | proportional to | y ∝ x |
| Δ | delta (change in, difference) | Δx = 5 − 2 = 3 |
| ⇒ | implies (if ... then) | a and b are odd ⇒ a+b is even |
| ⇔ | "if and only if" or iff or "is equivalent to" | x=y+1 ⇔ y=x−1 |
| ∴ | Therefore | a=b ∴ b=a |
| ∀ | For all (universal quantifier) | ∀x, x2 ≥ 0 |
| ∃ | there exists | ∃x such that x2 = 4 |
| Functions | ||
| √ | square root ("radical") | √4 = 2 |
 |
cube root | |
 |
nth root | |
| |x| | Absolute Value | |−3| = 3 |
| ! | Factorial | 4! = 4×3×2×1 = 24 |
| Σ | Sigma (sum of values in a range) | Σx for x = 1 to 4: 1 + 2 + 3 + 4 = 10 |
| Π | Capital Pi (product of values in a range) | Πx for x = 1 to 4: 1 × 2 × 3 × 4 = 24 |
| (f º g) | Function Composition | |
| Values | ||
| ∞ | Infinity | −∞ < x < ∞ |
| e | Euler's Number | e = 2.718... |
| π | Pi | circumference = 2πr |
| φ | Golden Ratio | φ = 1.618... |