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 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 3.17. 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.

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
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
\(\begin{array}{l}\frac{d^2 y}{d x^2}\end{array} \)	second derivative	derivative of derivative	\(\begin{array}{l}\frac{d^2 }{d x^2}(6x^{3}+x^{2}+3x+1) = 36x + 1\end{array} \)
dy/dx	derivative	derivative – Leibniz’s notation	\(\begin{array}{l}\frac{d }{d x}(5x) = 5\end{array} \)
\(\begin{array}{l}\frac{d^n y}{d x^n}\end{array} \)	nth derivative	n times derivation	n/a
\(\begin{array}{l}\ddot{y}= \frac{d^{2} y}{dt^{2}}\end{array} \)	Second derivative of time	derivative of derivative	n/a
\(\begin{array}{l}\dot{y}\end{array} \)	Single derivative of time	derivative by time – Newton’s notation	n/a
D2x	second derivative	derivative of derivative	n/a
Dx	derivative	derivative – Euler’s notation	n/a
∫	integral	opposite to derivation	n/a
\(\begin{array}{l}\frac{\ af(x,y)}{ax}\end{array} \)	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
\(\begin{array}{l}\vec{x}\end{array} \)	vector	\(\begin{array}{l}\vec{V} = x \hat{i} + y \hat{j} + z \hat{k}\end{array} \)	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:

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.

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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