MATHEMATICAL SYMBOLS

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mantrakshar	HINDI	Symbol Name	Meaning / definition	Example
=	बराबर चिह्न	equals sign	equality	5 = 2+3 ; 5 is equal to 2+3
≠	असमान चिन्ह	not equal sign	inequality	5 ≠ 4 ; 5 is not equal to 4
≈	लगभग समान	approximately equal	approximation	sin(0.01) ≈ 0.01, x ≈ y means x is approximately equal to y
>	सख्त असमानता	strict inequality	greater than	5 > 4; 5 is greater than 4
<	सख्त असमानता	strict inequality	less than	4 < 5;4 is less than 5
≥	असमानता	inequality	greater than or equal to	5 ≥ 4, x ≥ y means x is greater than or equal to y
≤	असमानता	inequality	less than or equal to	4 ≤ 5,x ≤ y means x is less than or equal to y
( )	छोटा कोष्टक	parentheses	calculate expression inside first	2 × (3+5) = 16
{ }	मझला कोष्ठक	flower brackets
[ ]	बड़ा कोष्ठक	brackets	calculate expression inside first	^[1] = 18
+	प्लस चिन्ह	plus sign	addition	1 + 1 = 2
−	घटाव चिन्ह	minus sign	subtraction	2 − 1 = 1
±	जोड़- घटाव चिन्ह	plus - minus	both plus and minus operations	3 ± 5 = 8 or -2
±	घटाव -जोड़ चिन्ह	minus - plus	both minus and plus operations	3 ∓ 5 = -2 or 8
*	तारांकन	asterisk	multiplication	2 * 3 = 6
×		times sign	multiplication	2 × 3 = 6
⋅	गुणन बिंदु	multiplication dot	multiplication	2 ⋅ 3 = 6
÷	विभाजन चिह्न	division sign / obelus	division	6 ÷ 2 = 3
/		division slash	division	6 / 2 = 3
—	क्षैतिज रेखा	horizontal line	division / fraction	\frac{6}{2}=3
mod	सापेक्ष	modulo	remainder calculation	7 mod 2 = 1
.	अवधि	period	decimal point, decimal separator	2.56 = 2+56/100
ab	शक्ति	power	exponent	23 = 8
$ a^b $	कैरट	caret	exponent	$ 2^3 = 8 $
√a	वर्गमूल	square root	√a ⋅ √a = a	√9 = ±3
3√a	घनमूल	cube root	3√a ⋅ 3√a ⋅ 3√a = a	3√8 = 2
4√a	चौथी जड़	fourth root	4√a ⋅ 4√a ⋅ 4√a ⋅ 4√a = a	4√16 = ±2
n√a	n-वें रूट (कट्टरपंथी)	n-th root (radical)		for n=3, n√8 = 2
%	प्रतिशत	percent	1% = 1/100	10% × 30 = 3
‰	प्रति-मिली	per-mille	1‰ = 1/1000 = 0.1%	10‰ × 30 = 0.3
ppm	प्रति मिलियन	per-million	1ppm = 1/1000000	10ppm × 30 = 0.0003
ppb	प्रति अरब	per-billion	1ppb = 1/1000000000	10ppb × 30 = 3×10-7
ppt	प्रति ट्रिलियन	per-trillion	1ppt = 10-12	10ppt × 30 = 3×10-10

Mantrakshar	Hindi	Symbol Name	Meaning / definition	Example
∠	कोण	angle	formed by two rays	∠ABC = 30°
	मापा कोण	measured angle		ABC = 30°
	गोलाकार कोण	spherical angle		AOB = 30°
∟	समकोण	right angle	= 90°	α = 90°
°	अंश	degree	1 turn = 360°	α = 60°
deg	अंश	degree	1 turn = 360deg	α = 60deg
′	प्रधान	prime	arcminute, 1° = 60′	α = 60°59′
″	द्वि प्रधान	double prime	arcsecond, 1′ = 60″	α = 60°59′59″
	रेखा	line	infinite line
AB	रेखा खंड	line segment	line from point A to point B
	किरण	ray	line that start from point A
	वृत्त चाप	arc	arc from point A to point B	= 60°
⊥	लंब	perpendicular	perpendicular lines (90° angle)	AC ⊥ BC
∥	समानांतर	parallel	parallel lines	AB ∥ CD
≅	सर्वगसम	congruent to	equivalence of geometric shapes and size	∆ABC≅ ∆XYZ
~	समानता / समरूप	similarity	same shapes, not same size	∆ABC~ ∆XYZ
Δ	त्रिकोण	triangle	triangle shape	ΔABC≅ ΔBCD
$$ delim{]}{x-y}{]} $$	दूरी	distance	distance between points x and y	$$ delim{]}{x-y = 5}{]} $$
π		pi constant	π = 3.141592654… is the ratio between the circumference and diameter of a circle	c = π⋅d = 2⋅π⋅r
rad		radians	radians angle unit	360° = 2π rad
c		radians	radians angle unit	360° = 2π c
grad		gradians / gons	grads angle unit	360° = 400 grad

Mantrakshar	Hindi	Symbol Name	Meaning / definition	Example
x	X चर	x variable	unknown value to find	when 2x = 4, then x = 2
≡	समानक	equivalence	identical to
≜	परिभाषा के बराबर	equal by definition	equal by definition
:=	परिभाषा के बराबर	equal by definition	equal by definition
~	लगभग समान	approximately equal	weak approximation	11 ~ 10
≈	लगभग समान	approximately equal	approximation	sin(0.01) ≈ 0.01
∝	आनुपातिक	proportional to	proportional to	y ∝ x when y = kx, k constant
∞	अनंत चिन्ह	lemniscate	infinity symbol
≪	से अधिक कम	much less than	much less than	1 ≪ 1000000
≫	से अधिक ज्यादा	much greater than	much greater than	1000000 ≫ 1
( )		parentheses	calculate expression inside first	2 * (3+5) = 16
[ ]		brackets	calculate expression inside first	^[2] = 18
{ }		braces	set
⌊x⌋	फर्श कोष्ठक	floor brackets	rounds number to lower integer	⌊4.3⌋ = 4
⌈x⌉	छत कोष्ठक	ceiling brackets	rounds number to upper integer	⌈4.3⌉ = 5
x!	विस्मयादिबोधक चिह्न	exclamation mark	factorial	4! = 123*4 = 24
delim{]}{x}{]}	लंबवत सलाखों	vertical bars	absolute value	FALSE
f (x)		function of x	maps values of x to f(x)	f (x) = 3x+5
(f ∘ g)		function composition	(f ∘ g) (x) = f (g(x))	f (x)=3x,g(x)=x-1 ⇒(f ∘ g)(x)=3(x-1)
(a,b)	खुला अंतराल	open interval	<m> (a,b) = {x	a < x < b} </m>	x∈ (2,6)
[a,b]	बंद अंतराल	closed interval	<m> [a,b] = {x	a ≤ x ≤ b} </m>	x ∈ [2,6]
∆	बदलाव चिन्ह	delta	change / difference	∆t = t1 - t0
∆		discriminant	Δ = b2 - 4ac
∑		sigma	summation - sum of all values in range of series	∑ xi= x1+x2+…+xn
∑∑		sigma	double summation
∏		capital pi	product - product of all values in range of series	∏ xi=x1∙x2∙…∙xn
e		e constant / Euler's number	e = 2.718281828…	e = lim (1+1/x)x , x→∞
γ		Euler-Mascheroni constant	γ = 0.5772156649…
φ	सुनहरा अनुपात	golden ratio	golden ratio constant
π		pi constant	π = 3.141592654…is the ratio between the circumference and diameter of a circle	c = π⋅d = 2⋅π⋅r

Symbol	Symbol Name	Meaning / definition	Example
·	dot	scalar product	a · b
×	cross	vector product	a × b
A⊗B	tensor product	tensor product of A and B	A ⊗ B
\langle x,y \rangle	inner product
[ ]	brackets	matrix of numbers
( )	parentheses	matrix of numbers
A	determinant	determinant of matrix A
det(A)	determinant	determinant of matrix A
<m>delim{vert}{x}{vert}</m>	double vertical bars	norm
AT	transpose	matrix transpose	(AT)ij = (A)ji
A†	Hermitian matrix	matrix conjugate transpose	(A†)ij = (A)ji
A*	Hermitian matrix	matrix conjugate transpose	(A*)ij = (A)ji
A -1	inverse matrix	A A-1 = I
rank(A)	matrix rank	rank of matrix A	rank(A) = 3
dim(U)	dimension	dimension of matrix A	dim(U) = 3

Probability and statistics

symbol	Symbol Name	Meaning / definition	Example
n!	factorial	n! = 1⋅2⋅3⋅…⋅n	5! = 1⋅2⋅3⋅4⋅5 = 120
nPk	permutation	_{n}P_{k}=\frac{n!}{(n-k)!}	5P3 = 5! / (5-3)! = 60
nCk	combination	_{n}C_{k}=\binom{n}{k}=\frac{n!}{k!(n-k)!}	5C3 = 5!/[3!(5-3)!]=10

SET THEORY SYMBOLS

Symbol	Symbol Name	Meaning / definition	Example
⋅	and	and	x ⋅ y
	caret / circumflex	and	$ x^y $
&	ampersand	and	x & y
+	plus	or	x + y
∨	reversed caret	or	x ∨ y
｜	vertical line	or	x ｜ y
x'	single quote	not - negation	x'
x	bar	not - negation	x
¬	not	not - negation	¬ x
!	exclamation mark	not - negation	! x
⊕	circled plus / oplus	exclusive or - xor	x ⊕ y
~	tilde	negation	~ x
⇒	implies
⇔	equivalent	if and only if (iff)
↔	equivalent	if and only if (iff)
∀	for all
∃	there exists
∄	there does not exists
∴	therefore
∵	because / since