We use the mathematical symbols for performing numerous operations in mathematics as well as in science. Moreover, these mathematical symbols make it much easier for us to refer the mathematical quantities and values. In addition, it also helps in an easier denotation. However, it’s quite interesting to notice that the whole of the maths is entirely based on these symbols and the numbers at the same time. Furthermore, these mathematical symbols not only refer to multiple quantities but also represent a relationship between 2 quantities. On the other hand, there are various symbols in mathematics that already have some predefined values.

**Importance of Mathematical Symbols**

- Mathematical symbols help us in denoting various quantities.
- It establishes the relationship between 2 different quantities.
- These symbols also helps in identifying the type of operation.
- These symbols make the reference much easier.
- The mathematical symbols are world-wide applicable and break the language barrier globally.

**Some Basic Mathematical Symbols with Names, Meaning, and Examples**

Symbol |
Name |
Meaning |
Example |

≠ |
not equal sign | inequality | 10 ≠ 6 |

= |
equals sign | equality | 3 = 1 + 2 |

< |
strict inequality | less than | 7 < 10 |

> |
strict inequality | greater than | 6 > 2 |

≤ |
inequality | less than or equal to | x ≤ y, means, y = x or y > x, but not vice-versa. |

≥ |
inequality | greater than or equal to | a ≥ b, means, a = b or a > b, but vice-versa does not hold true. |

[ ] |
brackets | calculate expression inside first | [ 2×5] + 7 = 17 |

( ) |
parentheses | calculate expression inside first | 3 × (3 + 7) = 30 |

− |
minus sign | subtraction | 5 − 2 = 3 |

+ |
plus sign | addition | 4 + 5 = 9 |

∓ |
minus – plus | both minus and plus operations | 1 ∓ 4 = -3 and 5 |

± |
plus – minus | both plus and minus operations | 5 ± 3 = 8 and 2 |

× |
times sign | multiplication | 4 × 3 = 12 |

* |
asterisk | multiplication | 2 * 3 = 6 |

÷ |
division sign / obelus | division | 15 ÷ 5 = 3 |

∙ |
multiplication dot | multiplication | 2 ∙ 3 = 6 |

– |
horizontal line | division / fraction | 8/2 = 4 |

/ |
division slash | division | 6 ⁄ 2 = 3 |

mod |
modulo | remainder calculation | 7 mod 3 = 1 |

a^{b} |
power | exponent | 2^{4} = 16 |

. |
period | decimal point, decimal separator | 4.36 = 4 +36/100 |

√a |
square root | √a · √a = a | √9 = ±3 |

a^b |
caret | exponent | 2 ^ 3 = 8 |

^{4}√a |
fourth root | ^{4}√a ·^{4}√a · ^{4}√a · ^{4}√a = a |
^{4}√16= ± 2 |

^{3}√a |
cube root | ^{3}√a ·^{3}√a · ^{3}√a = a |
^{3}√343 = 7 |

% |
per cent | 1% = 1/100 | 10% × 30 = 3 |

^{n}√a |
n-th root (radical) | ^{n}√a · ^{n}√a · · · n time = a |
for n=3, ^{n}√8 = 2 |

ppm |
per-million | 1 ppm = 1/1000000 | 10ppm × 30 = 0.0003 |

‰ |
per-mille | 1‰ = 1/1000 = 0.1% | 10‰ × 30 = 0.3 |

ppt |
per-trillion | 1ppt = 10-12 | 10ppt × 30 = 3×10-10 |

ppb |
per-billion | 1 ppb = 1/1000000000 | 10 ppb × 30 = 3×10-7 |

**Some Mathematical Logic Symbols with Name, Meaning, and Examples**

Symbol |
Name |
Meaning |
Example |

^ |
caret / circumflex | and | x ^ y |

· |
and | and | x · y |

+ |
plus | or | x + y |

& |
ampersand | and | x & y |

| |
vertical line | or | x | y |

∨ |
reversed caret | or | x ∨ y |

x |
bar | not – negation | x |

x‘ |
single-quote | not – negation | x’ |

! |
exclamation mark | not – negation | ! x |

¬ |
not | not – negation | ¬ x |

~ |
tilde | negation | ~ x |

⊕ |
circled plus / oplus | exclusive or – xor | x ⊕ y |

⇔ |
equivalent | if and only if (iff) | |

⇒ |
implies | n/a | n/a |

∀ |
for all | n/a | n/a |

↔ |
equivalent | if and only if (iff) | n/a |

∄ |
there does not exist | n/a | n/a |

∃ |
there exists | n/a | n/a |

∵ |
because / since | n/a | n/a |

∴ |
therefore | n/a | n/a |