# Important mathematical Symbols with name, meaning, and examples

June 18, 2022

**Mathematical symbols make mathematical operations easier. Here I have given the most important symbols being used in mathematics.**

Symbol | Read as | Meaning | Example | ||

≠ | not equal to | inequality | 7 ≠ 4 7 is not equal to 4 | ||

= | Equal to | equality | 10 + 12 = 22 22 is equal to 10 + 12 | ||

≈ | approximately equal | approximation | π≈3.14 | ||

> | strict inequality | greater than | 10 > 5 10 is greater than 5 | ||

< | strict inequality | less than | 9 < 12 9 is less than 12 | ||

( ) | parentheses | calculate expression inside first | 4 x (5-1) = 4 x 4 = 16 | ||

[ ] | brackets | calculate expression inside first | [(4+2)×(6+3)] + 2 = [6 x 9] + 2 = 54 + 2 = 56 | ||

+ | plus sign | addition | 1 + 1 = 2 | ||

− | minus sign | subtraction | 2 − 1 = 1 | ||

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

∓ | minus – plus | both minus and plus operations | 3 ∓ 5 = -2 or 8 | ||

* | asterisk | multiplication | 5 * 4= 20 | ||

× | times sign | multiplication | 9 x 3 = 27 | ||

⋅ | multiplication dot | multiplication | 3 . 6 = 18 | ||

÷ | division sign / obelus | division | 24 ÷ 6 = 4 | ||

≥ | inequality | greater than or equal to | 5 ≥ 4, x ≥ y means x is greater than or equal to y | ||

≤ | inequality | less than or equal to | 4 ≤ 5, x ≤ y means x is less than or equal to y | ||

/ | division slash | division | 8 / 2 = 4 | ||

— | horizontal line | division / fraction | |||

⇒ | material implication | implies | A⇒B means that if A is true, B must also be true, but if A is false, B is unknown. | ||

⇔ | material equivalence | if and only if | If A is true, B is true and if A is false, B is false. | ||

x^y | caret | exponent | 4 ^ 2 = 16 | ||

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

3√a | cube root | 3√a ⋅ 3√a ⋅ 3√a = a | 3√8 = 2 | ||

4√a | fourth root | 4√a ⋅ 4√a ⋅ 4√a ⋅ 4√a = a | 4√16 = ±2 | ||

n√a | n-th root (radical) | for n=3, n√8 = 2 | |||

% | percent | 2% = 2/100 | 2% × 30 = 3 | ||

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

≪ | is much less than | If x ≪y, x is much less than y. | 1≪999999999 | ||

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

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

|| | parallel | is parallel to | If A||B then A and B are parallel | ||

⊥ | perpendicular | is perpendicular to | If A⊥B then A is perpendicular to B | ||

≅ | congruence | is congruent to | If A≅B then shape A is congruent to shape B (has the same measurements) | ||

φ | golden ratio | golden ratio | φ =3.14159265358979…. | ||

∞ | infinity | infinity | ∞ is a symbol used to represent unending amounts. | ||

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

3√a | cube root | 3√a ⋅ 3√a ⋅ 3√a = a | 3√8 = 2 | ||

4√a | fourth root | 4√a ⋅ 4√a ⋅ 4√a ⋅ 4√a = a | 4√16 = ±2 | ||

n√a | n-th root (radical) | for n=3, n√8 = 2 | |||

mod | modulo | remainder calculation | 24 mod 7 = 3 | ||

. | period | decimal point, decimal separator | 4.345 = 4 + 345/1000 | ||

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