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MATHEMATICAL SYMBOLS
Basic math symbol
| 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 |
Geometry symbols
| 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 |
Algebra symbols
| 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! = 1*2*3*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 |
LINEAR Algebra symbols
| hindi | 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 symbols
| MANTRAKSHAR | HINDI | Symbol Name | Meaning / definition | Example |
|---|---|---|---|---|
| P(A) | प्रायिकता या संभाव्यता फलन | probability function | probability of event A | P(A) = 0.5 |
| P(A ⋂ B) | probability of events intersection | probability that of events A and B | P(A⋂B) = 0.5 | |
| P(A ⋃ B) | probability of events union | probability that of events A or B | P(A⋃B) = 0.5 | |
| {P(A vert B)} | conditional probability function | probability of event A given event B occured | P(A . B) = 0.3 | |
| f (x) | probability density function (pdf) | P(a ≤ x ≤ b) = ∫ f (x) dx | ||
| F(x) | cumulative distribution function (cdf) | F(x) = P(X≤ x) | ||
| μ | आबादी माध्य | population mean | mean of population values | μ = 10 |
| E(X) | expectation value | expected value of random variable X | E(X) = 10 | |
| E(X｜Y) | conditional expectation | expected value of random variable X given Y | E(X ｜Y=2) = 5 | |
| var(X) | प्रसरण | variance | variance of random variable X | var(X) = 4 |
| σ2 | प्रसरण | variance | variance of population values | σ2 = 4 |
| std(X) | मानक विचलन | standard deviation | standard deviation of random variable X | std(X) = 2 |
| σX | मानक विचलन | standard deviation | standard deviation value of random variable X | σX = 2 |
| median | middle value of random variable x | |||
| cov(X,Y) | सहप्रसरण | covariance | covariance of random variables X and Y | cov(X,Y) = 4 |
| corr(X,Y) | correlation | correlation of random variables X and Y | corr(X,Y) = 0.6 | |
| ρX,Y | correlation | correlation of random variables X and Y | ρX,Y = 0.6 | |
| ∑ | संकलन | summation | summation - sum of all values in range of series | |
| ∑∑ | double summation | double summation | ||
| Mo | बहुलक | mode | value that occurs most frequently in population | |
| MR | mid-range | MR = (xmax+xmin)/2 | ||
| Md | sample median | half the population is below this value | ||
| Q1 | lower / first quartile | 25% of population are below this value | ||
| Q2 | median / second quartile | 50% of population are below this value = median of samples | ||
| Q3 | upper / third quartile | 75% of population are below this value | ||
| x | sample mean | average / arithmetic mean | x = (2+5+9) / 3 = 5.333 | |
| s 2 | sample variance | population samples variance estimator | s 2 = 4 | |
| s | sample standard deviation | population samples standard deviation estimator | s = 2 | |
| zx | standard score | zx = (x-x) / sx | ||
| X ~ | distribution of X | distribution of random variable X | X ~ N(0,3) | |
| N(μ,σ2) | प्रसामान्य बंटन | normal distribution | gaussian distribution | X ~ N(0,3) |
| U(a,b) | uniform distribution | equal probability in range a,b | X ~ U(0,3) | |
| exp(λ) | exponential distribution | f (x) = λe-λx , x≥0 | ||
| gamma(c, λ) | gamma distribution | f (x) = λ c xc-1e-λx / Γ©, x≥0 | ||
| χ 2(k) | chi-square distribution | f (x) = xk/2-1e-x/2 / ( 2k/2 Γ(k/2) ) | ||
| F (k1, k2) | F distribution | |||
| Bin(n,p) | binomial distribution | f (k) = nCk pk(1-p)n-k | ||
| Poisson(λ) | Poisson distribution | f (k) = λke-λ / k! | ||
| Geom(p) | geometric distribution | f (k) = p(1-p) k | ||
| HG(N,K,n) | hyper-geometric distribution | |||
| Bern(p) | Bernoulli distribution |
Combinatorics Symbols
| HINDI | 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
| Hindi | Symbol | Symbol Name | Meaning / definition | Example |
|---|---|---|---|---|
| { } | set | a collection of elements | A = {3,7,9,14}, B = {9,14,28} | |
| A ∩ B | intersection | objects that belong to set A and set B | A ∩ B = {9,14} | |
| A ∪ B | union | objects that belong to set A or set B | A ∪ B = {3,7,9,14,28} | |
| A ⊆ B | subset | A is a subset of B. set A is included in set B. | {9,14,28} ⊆ {9,14,28} | |
| A ⊂ B | proper subset / strict subset | A is a subset of B, but A is not equal to B. | {9,14} ⊂ {9,14,28} | |
| A ⊄ B | not subset | set A is not a subset of set B | {9,66} ⊄ {9,14,28} | |
| A ⊇ B | superset | A is a superset of B. set A includes set B | {9,14,28} ⊇ {9,14,28} | |
| A ⊃ B | proper superset / strict superset | A is a superset of B, but B is not equal to A. | {9,14,28} ⊃ {9,14} | |
| A ⊅ B | not superset | set A is not a superset of set B | {9,14,28} ⊅ {9,66} | |
| 2A | power set | all subsets of A | ||
| \mathcal{P}(A) | power set | all subsets of A | ||
| A = B | equality | both sets have the same members | A={3,9,14}, B={3,9,14}, A=B | |
| Ac | complement | all the objects that do not belong to set A | ||
| A \ B | relative complement | objects that belong to A and not to B | A = {3,9,14}, B = {1,2,3},A-B = {9,14} | |
| A - B | relative complement | objects that belong to A and not to B | A = {3,9,14}, B = {1,2,3}, A-B = {9,14} | |
| A ∆ B | symmetric difference | objects that belong to A or B but not to their intersection | A = {3,9,14}, B = {1,2,3}, A ∆ B = {1,2,9,14} | |
| A ⊖ B | symmetric difference | objects that belong to A or B but not to their intersection | A = {3,9,14}, B = {1,2,3}, A ⊖ B = {1,2,9,14} | |
| a∈A | element of , belongs to | set membership | A={3,9,14}, 3 ∈ A | |
| x∉A | not element of | no set membership | A={3,9,14}, 1 ∉ A | |
| (a,b) | ordered pair | collection of 2 elements | ||
| A×B | cartesian product | set of all ordered pairs from A and B | A×B = {(a,b)｜a∈A , b∈B} | |
| ｜A｜ | cardinality | the number of elements of set A | A={3,9,14}, ｜A｜=3 | |
| #A | cardinality | the number of elements of set A | A={3,9,14}, #A=3 | |
| ｜ | vertical bar | such that | A={x｜3<x<14} | |
| aleph-null | infinite cardinality of natural numbers set | |||
| aleph-one | cardinality of countable ordinal numbers set | |||
| Ø | empty set | Ø = { } | C = {Ø} | |
| U} | universal set | set of all possible values | ||
| {N}0 | natural numbers / whole numbers set (with zero) | \mathbb{N}0 = {0,1,2,3,4,…} | 0 ∈ \mathbb{N}0 | |
| {N}1 | natural numbers / whole numbers set (without zero) | \mathbb{N}1 = {1,2,3,4,5,…} | 6 ∈ \mathbb{N}1 | |
| {Z} | integer numbers set | \mathbb{Z} = {…-3,-2,-1,0,1,2,3,…} | -6 ∈ \mathbb{Z} | |
| {Q} | rational numbers set | \mathbb{Q} = {x ｜ x=a/b, a,b∈\mathbb{Z}} | 2/6 ∈ \mathbb{Q} | |
| {R} | real numbers set | \mathbb{R} = {x ｜ -∞ < x <∞} | 6.343434∈\mathbb{R} | |
| {C} | complex numbers set | \mathbb{C} = {z ｜ z=a+bi, -∞<a<∞, -∞<b<∞} | 6+2i ∈ \mathbb{C} |
logic symbols
| Hindi | Symbol | Symbol Name | Meaning / definition | Example | ||
|---|---|---|---|---|---|---|
| ⋅ | and | and | x ⋅ y | |||
| <m> </m> | caret / circumflex | and | <m> x y </m> | |||
| & | 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 |
calculus and analysis symbols
| HINDI | Symbol | Symbol Name | Meaning / definition | Example | ||
|---|---|---|---|---|---|---|
| \lim_{x\to x0}f(x) | limit | limit value of a function | ||||
| ε | epsilon | represents a very small number, near zero | ε → 0 | |||
| e | e constant / Euler's number | e = 2.718281828… | e = lim (1+1/x)x , x→∞ | |||
| y' | derivative | derivative - Lagrange's notation | (3×3)' = 9×2 | |||
<m>y</m> | second derivative | derivative of derivative | (3×3) = 18x | ||||||
| y(n) | nth derivative | n times derivation | (3×3)(3) = 18 | |||
| <m>dy/dx</m> | derivative | derivative - Leibniz's notation | d(3×3)/dx = 9×2 | |||
| <m>d | 2y/dx | 2</m> | second derivative | derivative of derivative | d2(3×3)/dx2 = 18x | |
| <m>d | ny/dx | n</m> | nth derivative | n times derivation | ||
| \dot{y} | time derivative | derivative by time - Newton's notation | ||||
| time second derivative | derivative of derivative | |||||
| Dx y | derivative | derivative - Euler's notation | ||||
| Dx2y | second derivative | derivative of derivative | ||||
| <m>deltaf(x,y)/deltax</m> | partial derivative | ∂(x2+y2)/∂x = 2x | ||||
| ∫ | integral | opposite to derivation | ∫ f(x)dx | |||
| ∫∫ | double integral | integration of function of 2 variables | ∫∫ f(x,y)dxdy | |||
| ∫∫∫ | triple integral | integration of function of 3 variables | ∫∫∫ f(x,y,z)dxdydz | |||
| ∮ | closed contour / line integral | |||||
| ∯ | closed surface integral | |||||
| ∰ | closed volume integral | |||||
| [a,b] | closed interval | [a,b] = {x ｜ a ≤ x ≤ b} | ||||
| (a,b) | open interval | (a,b) = {x ｜ a < x < b} | ||||
| i | imaginary unit | i ≡ √-1 | z = 3 + 2i | |||
| z* | complex conjugate | z = a+bi → z*=a-bi | z* = 3 - 2i | |||
| z | complex conjugate | z = a+bi → z = a-bi | z = 3 - 2i | |||
| Re(z) | real part of a complex number | z = a+bi → Re(z)=a | Re(3 - 2i) = 3 | |||
| Im(z) | imaginary part of a complex number | z = a+bi → Im(z)=b | Im(3 - 2i) = -2 | |||
| ｜z｜ | absolute value/magnitude of a complex number | ｜z｜ = ｜a+bi｜= √(a2+b2) | ｜3 - 2i｜ = √13 | |||
| arg(z) | argument of a complex number | The angle of the radius in the complex plane | arg(3 + 2i) = 33.7° | |||
| ∇ | nabla / del | gradient / divergence operator | ∇f (x,y,z) | |||
| vector | ||||||
| unit vector | ||||||
| x * y | convolution | y(t) = x(t) * h(t) | ||||
| Laplace transform | F(s) = {f (t)} | |||||
| Fourier transform | X(ω) = {f (t)} | |||||
| δ | delta function | |||||
| ∞ | lemniscate | infinity symbol |
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