# List of mathematical symbols

meanings of symbols used in mathematics

The list below has some of the most common symbols in mathematics. However, these symbols can have other meanings in different contexts other than math.

Symbol | Name | Read as | Meaning | Example(s) |
---|---|---|---|---|

= | Equal | is equal to | If x=y, x and y represent the same value or thing. | 5(2)=10 |

≡ | Definition | is defined as | If x≡y, x is defined as another name of y | ϕ≡(√5+1)/2≈1.618 |

≈ | Approximately equal | is approximately equal to | If x≈y, x and y are almost equal. | √2≈1.41 |

≠ | Inequation | does not equal, is not equal to | If x≠y, x and y do not represent the same value or thing. | 1+1≠3 |

< | Strict inequality | is less than | If x<y, x is less than y. | 4<5 |

> | is greater than | If x>y, x is greater than y. | 3>2 | |

≪ | is much less than | If x≪y, x is much less than y. | 0.001≪999999999 | |

≫ | is much greater than | If x≫y, x is much greater than y. | 999999999≫0.001 | |

≤ | Inequality | is less than or equal to | If x≤y, x is less than or equal to y. | 5≤6 and 5≤5 |

≥ | is greater than or equal to | If x≥y, x is greater than or equal to y. | 2≥1 and 2≥2 | |

∝ | Proportionality | is proportional to | If x∝y, then y=kx for some constant k. | If y=4x then y∝x and x∝y |

+ | Addition | plus | x+y is the sum of x and y. | 2+3=5 |

- | Subtraction | minus | x-y is the subtraction of y from x | 5-3=2 |

× or · | Multiplication | times or multiplied by | x×y or x·y is the multiplication of x by y | 4×5=20 or 4·5=20 |

÷ or / | Division | divided by | x÷y or x/y is the division of x by y | 20÷4=5 or 20/4=5 |

± | Plus-minus | plus or minus | x±y means both x+y and x-y | 1±2 represents both 3 and -1 |

∓ | Minus-plus | minus or plus | 4±(3∓5) means both 4+(3-5) and 4-(3+5) | 6∓(1±3)=2 or 4 |

√ | Square root | square root | √x is a nonnegative number whose square is x. | √4=2 |

∑ | Summation | sum over … from … to … of, sigma | is the same as x_{1}+x_{2}+x_{3}+...+x_{n} | |

∏ | Product | product over … from … to … of | is the same as x_{1}×x_{2}×x_{3}×....×x_{n} | =1×2×3×4×5=120 |

! | Factorial | factorial | n! is the product 1×2×3...×n | 5!=1×2×3×4×5=120 |

⇒ | Material implication | implies | A⇒B means that if A is true, B must also be true, but if A is false, B is unknown. | x=3⇒x^{2}=9, but x^{2}=9⇒x=3 is false, because x could also be -3. |

⇔ | Material equivalence | if and only if | If A is true, B is true and if A is false, B is false. | x=y+1⇔x-1=y |

|…| | Absolute value | absolute value of | |x| is the distance along the real line (or across the complex plane) between x and zero. | |x|=x and |-x|=x |

|| | Parallel | is parallel to | If A||B then line A will never touch line B, thus both lines are rotated in the same angle. | x||(x+1) |

⊥ | Perpendicular | is perpendicular to | If A⊥B then line A is touching line B in a 90 degrees angle. | x⊥y |

≅ | Congruence | is congruent to | If A≅B then shape A and B same shape and size, or A has the same shape and size as the mirror image of B. | If two triangles, △ABC and △DEF, are congruent, it can be denoted as △ABC≅△DEF |

φ | Golden ratio | golden ratio | The golden ratio is an irrational number equal to (1+√5)÷2 or approximately 1.6180339887. | φ ≈ 1.6180339887 |

∞ | Infinity | infinity | ∞ is a symbol used to represent unending amounts. | ∞ + x = ∞ |

∈ | Set membership | is an element of | a∈S means that a is an element of the set S | 3.5∈ℝ, 1∈ℕ, 1+i∈ℂ |

∉ | is not an element of | a∉S means that a is not an element of the set S | 2.1∉ℕ, 1+i∉ℝ | |

{,} | Set brackets | the set of | {a,b,c} is the set consisting of a, b, and c | S = { a, b, c } |

ℕ | Natural numbers | N | ℕ denotes the set of natural numbers | 1∈ℕ, 2∈ℕ, 100∈ℕ |

ℤ | Integers | Z | ℤ denotes the set of integers | -1∈ℤ, 0∈ℤ, 30∈ℤ |

ℚ | Rational numbers | Q | ℚ denotes the set of rational numbers | 8.323∈ℚ, 7∈ℚ, π∉ℚ |

ℝ | Real numbers | R | ℝ denotes the set of real numbers | π∈ℝ, 7∈ℝ, √(-1)∉ℝ |

ℂ | Complex numbers | C | ℂ denotes the set of complex numbers | √(-1)∈ℂ |

x̄ | Mean | bar, overbar | x̄ is the mean (average) of x_{i} | if x={1,2,3} then x̄=2 |

x̄ | Complex conjugate | the complex conjugate of x | If x=a ± bi, then x̄=a ∓ bi where i=√(-1) | x=-4 + 5.3i, x̄=-4 - 5.3i |

[+|-] | Situational plus minus | Either plus or minus depending on the situation. | If y=[+|-]x then x is either positive or negative depending on the situation. | y=[+|-]x y equals either +x or -x depending on the scenario. |

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