Mathematical Symbols

Mathematical symbols are used to perform various operations. The symbols make it easier to refer Mathematical 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 full name of Maths is Mathematics. It is defined as the science of calculating, measuring, quantity, shape, and structure. It is based on logical thinking, numerical calculations, and the study of shapes. Algebra, trigonometry, geometry, and number theory are examples of mathematical dimensions, and 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 3.14. 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.

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
=	equal 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 = 10 + 7 =  17
( )	parentheses	calculate expression inside first	3 × (3 + 7) = 3 × 10 = 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
ab	power	exponent	24 = 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
X̄	bar	not – negation	x̄
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)	p: this year has 366 days q: this is a leap year p ⇔ q
⇒	implies	Implication	p: a number is a multiple of 4 q: the number is even p ⇒ q
∈	Belong to/is an element of	Set membership	A = {1, 2, 3} 2 ∈ A
∉	Not element of	Negation of set membership	A={1, 2, 3} 0 ∉ A
∀	for all	Universal Quantifier	2n is even ∀ n ∈ N where N is a set of Natural Numbers
↔	equivalent	if and only if (iff)	p: x is an even number q: x is divisible by 2 p ↔ q
∄	there does not exist	Negation of existential quantifier	b is not divisible by a, then ∄ n ∈ N such that b = na
∃	there exists	Existential quantifier	b is divisible by a, then ∃ n ∈ N such that b = na
∵	because / since	Because shorthand	a = b, b = c ⇒ a = c (∵ a = b)
∴	therefore	Therefore shorthand (Logical consequence)	x + 6 = 10 ∴ x = 4

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
limx→a	limit	limit value of a function	limx→a(3x+1)= 3 × a + 1 = 3a + 1
y ‘	derivative	derivative – Lagrange’s notation	(5x3)’ = 15x2
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 3xn = 3 n (n-1)(n-2)….(2)(1)= 3n!
y”	second derivative	derivative of derivative	(4x3)” = 24x
$\begin{array}{l}\frac{{�}^2�}{�{�}^2}\end{array}$	second derivative	derivative of derivative	$\begin{array}{l}\frac{{�}^2}{�{�}^2}(6{�}^3+{�}^2+3�+1)=36�+1\end{array}$
dy/dx	derivative	derivative – Leibniz’s notation	$\begin{array}{l}\frac{�}{��}(5�)=5\end{array}$
$\begin{array}{l}\frac{{�}^{�}�}{�{�}^{�}}\end{array}$	nth derivative	n times derivation	$\begin{array}{l}\frac{{�}^{�}�}{�{�}^{�}}({�}^{�})=�!\end{array}$
$\begin{array}{l}\ddot{�}=\frac{{�}^2�}{�{�}^2}\end{array}$	Second derivative of time	derivative of derivative	If y = 4t2, then $\begin{array}{l}\ddot{�}=\frac{{�}^2�}{�{�}^2}=4\frac{{�}^2}{�{�}^2}({�}^2)=8\end{array}$
$\begin{array}{l}\dot{�}\end{array}$	Single derivative of time	derivative by time – Newton’s notation	y = 5t, then  $\begin{array}{l}\dot{�}=\frac{��}{��}=5\frac{�}{��}(�)=5\end{array}$
D2x	second derivative	derivative of derivative	y” + 2y + 1 = 0 ⇒ D2y + 2Dy + 1 = 0
Dx	derivative	derivative – Euler’s notation	dy/x – 1 = 0 ⇒ Dy – 1 = 0
∫	integral	opposite to derivation	∫xn dx = xn + 1/n + 1  +  C
$\begin{array}{l}\frac{��(�,�)}{��}\end{array}$	partial derivative	Differentiating a function with respect to one variable considering the other variables as constant	∂(x2+y2)/∂x = 2x
∭	triple integral	integration of the function of 3 variables	$\begin{array}{l}{\int }_1^2{\int }_2^3{\int }_0^1(���)������\end{array}$
∬	double integral	integration of the function of 2 variables	∬(x3+y3)dx dy
∯	closed surface integral	Double integral over a closed surface	∭V (⛛.F)dV = ∯S (F.n̂) dS
∮	closed contour / line integral	Line integral over closed curve	∮C 2/z dz
[a,b]	closed interval	[a,b] = {x | a ≤ x ≤ b}	sin x ∈ [ – 1, 1]
∰	closed volume integral	Volume integral over a closed three-dimensional domain	∰ (x2 + y2 + z2) dx dy dz
(a,b)	open interval	(a,b) = {x | a < x < b}	f is continuous within (0, 1)
z*	complex conjugate	z = a+bi → z*=a-bi	If z = 3 + 2i then z* = 3 – 2i
i	imaginary unit	i ≡ √-1	z = 3 + 2i
∇	nabla / del	gradient / divergence operator	∇f (x,y,z)
$\begin{array}{l}\overrightarrow{�}\end{array}$	vector	A quantity with magnitude and direction	$\begin{array}{l}\overrightarrow{�}=�\widehat{�}+�\widehat{�}+�\widehat{�}\end{array}$
x * y	convolution	Modification in a function due to the other function.	y(t) = x(t) * h(t)
∞	lemniscate	infinity symbol	3x ≥ 0; x ∈ (0, ∞)
δ	delta function	Dirac Delta function	$\begin{array}{l}�(�)=\{\begin{array}{cc}0& ���\ne 0\\ \mathrm{\infty }& ���=0\end{array}\end{array}$

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:

Symbol	Symbol Name	Meaning or Definition	Example
nPk	Permutation	$\begin{array}{l}{}^{�}{�}_{�}=\frac{�!}{(�-�)!}\end{array}$	$\begin{array}{l}{}^5{�}_3=\frac{5!}{(5-3)!}=60\end{array}$
n!	Factorial	n! = 1×2×3×…×n	5! = 1×2×3×4×5 = 120
nCk	Combination	$\begin{array}{l}{}^{�}{�}_{�}=\frac{�!}{�!(�-�)!}\end{array}$	$\begin{array}{l}{}^5{�}_3=\frac{5!}{3!(5-3)!}=10\end{array}$

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 Roman numeral symbols used in Maths are as follows.

Name	European	Roman	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 

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