# Mathematical Symbols

**Mathematical symbols** are used to perform various operations. The symbols make it easier to refer Maths quantities. It is interesting to note that Mathematics is completely based on numbers and symbols. The **math symbols** not only refer to different quantities but also represent the relationship between two quantities. All mathematical symbols are mainly used to perform mathematical operations under various concepts. As we know, the concept of maths is purely dependent on numbers and symbols.

There are many symbols used in Maths that have some predefined values. To simplify the expressions, we can use those kinds of values instead of those symbols. Some of the examples are the **pi symbol** (**π), **which holds the value 22/7 or 3.17. The pi symbol is a mathematical constant which is defined as the ratio of circumference of a circle to its diameter. In Mathematics, pi symbol is also referred to as Archimedes constant. Also, **e-symbol in Maths** which holds the value** e= 2.718281828….**This symbol is known as e-constant or Euler’s constant. The table provided below has a list of all the common symbols in Maths with **meaning and examples**.

There are so many mathematical symbols that are very important to students. To understand this in an easier way, the list of mathematical symbols are noted here with definition and examples. There are numerous signs and symbols, ranging from the simple addition concept sign to the complex integration concept sign. Here, the list of mathematical symbols is provided in a tabular form, and those notations are categorized according to the concept.

**List of Mathematical Symbols**

- Basic Math Symbols
- Logic Symbols
- Calculus and Analysis Symbols
- Combinatorics Symbols
- Greek Alphabets
- Common Numeral Symbols
- Importance
- FAQs

## Basic Mathematical Symbols With Name, Meaning and Examples

The basic mathematical symbols used in Maths help us to work with mathematical concepts in a theoretical manner. In simple words, without symbols, we cannot do maths. The mathematical signs and symbols are considered as representative of the value. The basic symbols in maths are used to express mathematical thoughts. The relationship between the sign and the value refers to the fundamental need of mathematics. With the help of symbols, certain concepts and ideas are clearly explained. Here is a list of commonly used mathematical symbols with names and meanings. Also, an example is provided to understand the usage of mathematical symbols.

Symbol | Symbol Name in Maths | Math Symbols 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 |

% |
percent | 1% = 1/100 | 10% × 30 = 3 |

^{n}√a |
n-th root (radical) | ^{n}√a · ^{n}√a · · · n times = 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 |

## Maths Logic symbols With Meaning

Symbol | Symbol Name in Maths | Math Symbols 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 |

## Calculus and Analysis Symbol Names in Maths

In calculus, we have come across different math symbols. All mathematical symbols with names and meanings are provided here. Go through the all mathematical symbols used in calculus.

Symbol | Symbol Name in Maths | Math Symbols Meaning | Example |
---|---|---|---|

ε |
epsilon | represents a very small number, near-zero | ε → 0 |

lim_{x→a} |
limit | limit value of a function | lim_{x→a}(3x+1)= 3 × a + 1 = 3a + 1 |

y ‘ |
derivative | derivative – Lagrange’s notation | (5x^{3})’ = 15x^{2} |

e |
e constant / Euler’s number | e = 2.718281828… | e = lim (1+1/x)x , x→∞ |

y(n) |
nth derivative | n times derivation | nth derivative of 3x^{n} = 3 n (n-1)(n-2)….(2)(1)= 3n! |

y” |
second derivative | derivative of derivative | (4x^{3})” = 24x |

\(\frac{d^2 y}{d x^2}\) |
second derivative | derivative of derivative | \(\frac{d^2 }{d x^2}(6x^{3}+x^{2}+3x+1) = 36x + 1\) |

dy/dx |
derivative | derivative – Leibniz’s notation | \(\frac{d }{d x}(5x) = 5\) |

\(\frac{d^n y}{d x^n}\) |
nth derivative | n times derivation | n/a |

\(\ddot{y}= \frac{d^{2} y}{dt^{2}}\) |
Second derivative of time | derivative of derivative | n/a |

\(\dot{y}\) |
Single derivative of time | derivative by time – Newton’s notation | n/a |

D^{2}x |
second derivative | derivative of derivative | n/a |

Dx |
derivative | derivative – Euler’s notation | n/a |

∫ |
integral | opposite to derivation | n/a |

\(\frac{\ af(x,y)}{ax}\) |
partial derivative | ∂(x2+y2)/∂x = 2x | n/a |

∭ |
triple integral | integration of the function of 3 variables | n/a |

∬ |
double integral | integration of the function of 2 variables | n/a |

∯ |
closed surface integral | n/a | n/a |

∮ |
closed contour / line integral | n/a | n/a |

[a,b] |
closed interval | [a,b] = {x | a ≤ x ≤ b} | n/a |

∰ |
closed volume integral | n/a | |

(a,b) |
open interval | (a,b) = {x | a < x < b} | n/a |

z* |
complex conjugate | z = a+bi → z*=a-bi | z* = 3 + 2i |

i |
imaginary unit | i ≡ √-1 | z = 3 + 2i |

∇ |
nabla / del | gradient / divergence operator | ∇f (x,y,z) |

z |
complex conjugate | z = a+bi → z = a-bi | z = 3 + 2i |

\(\vec{x}\) |
vector | \(\vec{V} = x \hat{i} + y \hat{j} + z \hat{k}\) | n/a |

x * y |
convolution | y(t) = x(t) * h(t) | n/a |

∞ |
lemniscate | infinity symbol | n/a |

δ |
delta function | n/a | n/a |

## Combinatorics Symbols Used in Maths

The different Combinatorics symbols used in maths concern the study of the combination of finite discrete structures. Some of the most important combinatorics symbols used in maths are as follows:

### Greek Alphabet Letters Used in Maths

Mathematicians frequently use Greek alphabets in their work to represent the variables, constants, functions and so on. Some of the commonly used Greek symbols name in Maths are listed below:

Greek Symbol | Greek Letter Name | English Equivalent | Pronunciation | |
---|---|---|---|---|

## Upper Case |
## Lower Case |
|||

Β | β | Beta | b | be-ta |

Α | α | Alpha | a | al-fa |

Δ | δ | Delta | d | del-ta |

Γ | γ | Gamma | g | ga-ma |

Ζ | ζ | Zeta | z | ze-ta |

Ε | ε | Epsilon | e | ep-si-lon |

Θ | θ | Theta | th | te-ta |

Η | η | Eta | h | eh-ta |

Κ | κ | Kappa | k | ka-pa |

Ι | ι | Iota | i | io-ta |

Μ | μ | Mu | m | m-yoo |

Λ | λ | Lambda | l | lam-da |

Ξ | ξ | Xi | x | x-ee |

Ν | ν | Nu | n | noo |

Ο | ο | Omicron | o | o-mee-c-ron |

Π | π | Pi | p | pa-yee |

Σ | σ | Sigma | s | sig-ma |

Ρ | ρ | Rho | r | row |

Υ | υ | Upsilon | u | oo-psi-lon |

Τ | τ | Tau | t | ta-oo |

Χ | χ | Chi | ch | kh-ee |

Φ | φ | Phi | ph | f-ee |

Ω | ω | Omega | o | o-me-ga |

Ψ | ψ | Psi | ps | p-see |

## Common Numeral Symbols Used in Maths

The roman numerals are used in many applications and can be seen in our real-life activities. The common numeral symbols used in Maths are as follows.

Name | European | Roman | Hindu Arabic | Hebrew |
---|---|---|---|---|

zero |
0 | n/a | 0 | n/a |

one |
1 | I | ١ | א |

two |
2 | II | ٢ | ב |

three |
3 | III | ٣ | ג |

four |
4 | IV | ٤ | ד |

five |
5 | V | ٥ | ה |

six |
6 | VI | ٦ | ו |

seven |
7 | VII | ٧ | ז |

eight |
8 | VIII | ٨ | ח |

nine |
9 | IX | ٩ | ט |

ten |
10 | X | ١٠ | י |

eleven |
11 | XI | ١١ | יא |

twelve |
12 | XII | ١٢ | יב |

thirteen |
13 | XIII | ١٣ | יג |

fourteen |
14 | XIV | ١٤ | יד |

fifteen |
15 | XV | ١٥ | טו |

sixteen |
16 | XVI | ١٦ | טז |

seventeen |
17 | XVII | ١٧ | יז |

eighteen |
18 | XVIII | ١٨ | יח |

nineteen |
19 | XIX | ١٩ | יט |

twenty |
20 | XX | ٢٠ | כ |

thirty |
30 | XXX | ٣٠ | ל |

forty |
40 | XL | ٤٠ | מ |

fifty |
50 | L | ٥٠ | נ |

sixty |
60 | LX | ٦٠ | ס |

seventy |
70 | LXX | ٧٠ | ע |

eighty |
80 | LXXX | ٨٠ | פ |

ninety |
90 | XC | ٩٠ | צ |

one hundred |
100 | C | ١٠٠ | ק |

These are some of the most important and commonly used symbols in mathematics. It is important to get completely acquainted with all the maths symbols to be able to solve maths problems efficiently. It should be noted that without knowing maths symbols, it is extremely difficult to grasp certain concepts on a universal scale. Some of the key importance of maths symbols are summarized below.

### Importance of Mathematical Symbols

- Helps in denoting quantities
- Establishes relationships between quantities
- Helps to identify the type of operation
- Makes reference easier
- Maths symbols are universal and break the language barrier

## Frequently Asked Questions on Math Symbols

### What is pi symbol in Maths?

The pi symbol is a mathematical constant, which is approximately equal to 3.14. The symbol of pi is π and it is a Greek alphabet. Pi is an irrational number which is defined as the ratio of circle circumference to its diameter.

### What is e symbol in mathematics?

The “e” symbol in maths represents Euler’s number which is approximately equal to 2.71828…It is considered as one of the most important numbers in mathematics. It is an irrational number and it cannot be represented as a simple fraction

### Write down the symbols for basic arithmetic operations.

The symbols for basic arithmetic operations are addition (+), subtraction (-), Multiplication (×), Division(÷).

### Why do we use mathematical symbols?

Mathematics is a universal language and the basics of maths are the same everywhere in the universe. Mathematical symbols play a major role in this. The definition and the value of the symbols are constant. For example, the Roman letter X represents the value 10 everywhere around us.

### Mention the logic symbols in maths.

The logic symbols in maths are:

AND (^)

OR (∨)

NOT (¬)

Implies (⇒)

Equivalent (⇔)

For all (∀)

There exists (∃)

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