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| mathematical_symbols [2023/01/03 09:49] – [calculus and analysis symbols] brahmantra | mathematical_symbols [2023/06/08 07:17] () – removed brahmantra | ||
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| - | ====== MATHEMATICAL SYMBOLS ====== | ||
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| - | ==== Basic math symbol ==== | ||
| - | |||
| - | ^ mantrakshar | ||
| - | | = | ||
| - | | ≠ | ||
| - | | ≈ | ||
| - | | > | ||
| - | | < | ||
| - | | ≥ | ||
| - | | ≤ | ||
| - | | ( ) | ||
| - | | { } | ||
| - | | [ ] | ||
| - | | + | ||
| - | | − | ||
| - | | ± | ||
| - | | ± | ||
| - | | * | ||
| - | | × | ||
| - | | ⋅ | ||
| - | | ÷ | ||
| - | | / | ||
| - | | — | ||
| - | | mod | ||
| - | | . | ||
| - | | ab | शक्ति | ||
| - | | $ a^b $ | कैरट | ||
| - | | √a | वर्गमूल | ||
| - | | 3√a | ||
| - | | 4√a | ||
| - | | n√a | ||
| - | | % | ||
| - | | ‰ | ||
| - | | ppm | ||
| - | | ppb | ||
| - | | ppt | ||
| - | |||
| - | ==== Geometry symbols ==== | ||
| - | |||
| - | |||
| - | ^ Mantrakshar | ||
| - | | ∠ | ||
| - | | | मापा कोण | ||
| - | | | गोलाकार कोण | ||
| - | | ∟ | ||
| - | | ° | ||
| - | | deg | ||
| - | | ′ | ||
| - | | ″ | ||
| - | | | रेखा | ||
| - | | AB | रेखा खंड | ||
| - | | | किरण | ||
| - | | | वृत्त चाप | ||
| - | | ⊥ | ||
| - | | ∥ | ||
| - | | ≅ | ||
| - | | ~ | ||
| - | | Δ | ||
| - | | $$ delim{]}{x-y}{]} $$ | दूरी | ||
| - | | π | ||
| - | | rad | ||
| - | | c | ||
| - | | grad | | gradians / gons | grads angle unit | 360° = 400 grad | | ||
| - | |||
| - | ==== Algebra symbols ==== | ||
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| - | ^ 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 | | | ||
| - | | : | ||
| - | | ~ | 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, | ||
| - | | ∞ | 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 | [(1+2)*(1+5)] = 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, | ||
| - | | (a, | ||
| - | | [a, | ||
| - | | ∆ | 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' | ||
| - | | 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 | | ||
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| - | ==== 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 | | | ||
| - | | | < | ||
| - | | | 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 | | ||
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| - | ==== Probability and statistics symbols ==== | ||
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| - | ^ 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, | ||
| - | | corr(X, | ||
| - | | ρX, | ||
| - | | ∑ | 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)/ | ||
| - | | 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, | ||
| - | | N(μ, | ||
| - | | U(a, | ||
| - | | exp(λ) | | exponential distribution | f (x) = λe-λx , | ||
| - | | gamma(c, λ) | | gamma distribution | f (x) = λ c xc-1e-λx / | ||
| - | | χ 2(k) | | chi-square distribution | f (x) = xk/ | ||
| - | | F (k1, k2) | | F distribution | | | | ||
| - | | Bin(n, | ||
| - | | Poisson(λ) | | Poisson distribution | f (k) = λke-λ / | ||
| - | | Geom(p) | | geometric distribution | f (k) = p(1-p) k | | | ||
| - | | HG(N, | ||
| - | | Bern(p) | | Bernoulli distribution | | | | ||
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| - | ==== Combinatorics Symbols ==== | ||
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| - | ^ HINDI ^ symbol | ||
| - | | | n! | factorial | ||
| - | | | nPk | ||
| - | | | nCk | ||
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| - | ==== set theory symbols ==== | ||
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| - | ^ Hindi ^ Symbol | ||
| - | | | { } | ||
| - | | | A ∩ B | ||
| - | | | A ∪ B | ||
| - | | | A ⊆ B | ||
| - | | | A ⊂ B | ||
| - | | | A ⊄ B | ||
| - | | | A ⊇ B | ||
| - | | | A ⊃ B | ||
| - | | | A ⊅ B | ||
| - | | | 2A | power set | all subsets of A | ||
| - | | | \mathcal{P}(A) | ||
| - | | | A = B | ||
| - | | | Ac | complement | ||
| - | | | A \ B | ||
| - | | | A - B | ||
| - | | | A ∆ B | ||
| - | | | A ⊖ B | ||
| - | | | a∈A | ||
| - | | | | | ||
| - | | | x∉A | ||
| - | | | (a,b) | ||
| - | | | A×B | cartesian product | ||
| - | | | ｜A｜ | ||
| - | | | #A | cardinality | ||
| - | | | ｜ | vertical bar | ||
| - | | | | aleph-null | ||
| - | | | | aleph-one | ||
| - | | | Ø | ||
| - | | | U} | universal set | set of all possible values | ||
| - | | | {N}0 | natural numbers / whole numbers set (with zero) | ||
| - | | | {N}1 | natural numbers / whole numbers set (without zero) | \mathbb{N}1 = {1, | ||
| - | | | {Z} | ||
| - | | | {Q} | ||
| - | | | {R} | ||
| - | | | {C} | ||
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| - | ==== logic symbols ==== | ||
| - | |||
| - | ^ Hindi ^ Symbol | ||
| - | | | ⋅ | and | and | ||
| - | | | | caret / circumflex | ||
| - | | | & | ampersand | ||
| - | | | + | plus | ||
| - | | | ∨ | reversed caret | ||
| - | | | ｜ | ||
| - | | | x' | ||
| - | | | x | bar | not - negation | ||
| - | | | ¬ | not | not - negation | ||
| - | | | ! | exclamation mark | ||
| - | | | ⊕ | circled plus / oplus | ||
| - | | | ~ | tilde | negation | ||
| - | | | ⇒ | implies | ||
| - | | | ⇔ | equivalent | ||
| - | | | ↔ | equivalent | ||
| - | | | ∀ | for all | | | ||
| - | | | ∃ | there exists | ||
| - | | | ∄ | there does not exists | ||
| - | | | ∴ | therefore | ||
| - | | | ∵ | because / since | | | ||
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| - | ==== calculus and analysis symbols ==== | ||
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| - | ^ HINDI ^ Symbol | ||
| - | | | $ \lim_{x\to x0}f(x) | ||
| - | | | ε | epsilon | ||
| - | | | e | e constant / Euler' | ||
| - | | | y' | ||
| - | | | $ y'' | ||
| - | | | y(n) | nth derivative | ||
| - | | | $ dy/dx $ | ||
| - | | | $d^2y/dx^2 $ | second derivative | ||
| - | | | $ d^ny/dx^n $ | nth derivative | ||
| - | | | $ \dot{y} $ | time derivative | ||
| - | | | | ||
| - | | | $ D_{\text{x}}y $ | ||
| - | | | $ D_{\text{x^2}}y $ | ||
| - | | | $ deltaf(x, | ||
| - | | | ∫ | integral | ||
| - | | | ∫∫ | ||
| - | | | ∫∫∫ | ||
| - | | | ∮ | closed contour / line integral | ||
| - | | | ∯ | closed surface integral | ||
| - | | | ∰ | closed volume integral | ||
| - | | | [a,b] | closed interval | ||
| - | | | (a,b) | open interval | ||
| - | | | i | imaginary unit | i ≡ √-1 | ||
| - | | | z* | ||
| - | | | z | complex conjugate | ||
| - | | | Re(z) | real part of a complex number | ||
| - | | | Im(z) | imaginary part of a complex number | ||
| - | | | ｜z｜ | ||
| - | | | arg(z) | ||
| - | | | ∇ | nabla / del | ||
| - | | | | ||
| - | | | | ||
| - | | | x * y | ||
| - | | | | ||
| - | | | | ||
| - | | | δ | delta function | ||
| - | | | ∞ | lemniscate | ||
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