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X ~ N(0,1), the standard normal distribution x > y means x is greater than y. 3 < 4 (If the change becomes infinitesimal, d and even d are used instead. Not to be confused with the symmetric difference, written ?, above.) \tfrac{\Delta y}{\Delta x} is the gradient of a straight line. is perpendicular to Index of Unicode symbols ? = wavefunction of the system set theory \frac{73!/(73-5)!}{5!} =: h = Plancks constant 8 is an element of the extended number line that is greater than all real numbers; it often occurs in limits. \lim_{x\to 0} \frac{1}{|x|} = \infty max; is comparable to Functional derivative of is row equivalent to It is important to note that x ? y remains true if every element is equal. However, if the operator is changed, x = y is true if and only if x ? y is also true. direct sum of minus-plus everywhere ? 2713 check mark × 00D7 multiplication sign definition ?? 1F4C9 chart with downward trend ? 23EB Black up-pointing double triangle \begin{align} \Phi(\mathbf{p},s_z,t) & = \frac{1}{\sqrt{2\pi\hbar}} \int\limits_{\mathrm{all \, space}} e^{-i\mathbf{p}\cdot\mathbf{r}/\hbar} \Psi(\mathbf{r}, s_z,t)\mathrm{d}^3\mathbf{r} \\ ? 2104 Centerline symbol [ , , ] Ceština ? 23EB Black up-pointing double triangle ? 2260 ne, NotEqual, not equal to is defined as; \oint \!\, the dual of ... G. A. G. Bennet (1974). Electricity and Modern Physics (2nd ed.). Edward Arnold (UK). ISBN 0-7131-2459-8. linear algebra image of ... under ... (subset) A ? B means every element of A is also an element of B.[5] orthogonal complement ? 20B1 Peso \mid\mid \!\, 37 P(Ei) = probability of energy Ei En = energy eigenvalue the (set of) natural numbers ? a ~ b means b \in [a] (and equivalently a \in [b]). 1 ~ 5 mod 4 ? 2244 not asymptotically equal to ? 25AD rectangle 2000 ? 266F music sharp sign V = potential energy, The direct sum is a special way of combining several objects into one general object. am { ?u,v? means the inner product of u and v, where u and v are members of an inner product space. ? 2031 Basis point, per ten thousand, permyriad ?? 1F315 full moon |x| means the (Euclidean) length of vector x. For x = (3,-4) right-open interval Norsk nynorsk ? = F = momentum-space wavefunction V \otimes U means the tensor product of V and U.[12] V \otimes_R U means the tensor product of modules V and U over the ring R. {1, 2, 3, 4} ? {1, 1, 2} = inner product of (This is I. M. Vinogradovs notation. Another notation is the Big O notation, which looks like f = O(g).) x « ex ? 2713 Check mark V Dirac notation This last equation is in a very high dimension,[2] so the solutions are not easy to visualize. such that; downwards zigzag arrow knot composition of closed line integral in TeX Name Explanation Examples ? 2191 up arrow 17:00 are in the same equivalence class (a, b, c) is an ordered triple (or 3-tuple). U = -\boldsymbol{\mu}\cdot\mathbf{B} = -\mu_z B\,\! the direct product of ? 2031 Basis point, per ten thousand, permyriad 0&0 \\ \frac{d}{dt}\hat{A}(t)=\frac{i}{\hbar}[\hat{H},\hat{A}(t)]+\frac{\partial \hat{A}(t)}{\partial t}, [ x ? y means that x is comparable to y. {e, p} ? {1, 2, e, 3, p} under set containment. L1 ? L2 means that the problem L1 is Karp reducible to L2.[2] If L1 ? L2 and L2 ? P, then L1 ? P. & = -\frac{\hbar^2}{2m}\nabla^2 + V(\mathbf{r},t) \\ ? |\ \rangle \!\, ? 2662 rhombus, diamond Conversion of units History of the metric system Metric prefixes Proposed redefinitions Systems of measurement := \!\, natural join [x] means the nearest integer to x. Symbol e = electron charge ?M means the boundary of M ?{x : ||x|| = 2} = {x : ||x|| = 2} complex numbers 5% i\hbar\frac{\partial}{\partial t} \Psi = \hat{H}\Psi minus; P(E_i) = g(E_i)/(e^{(E-\mu)/kT}+1)\,\! 44 Time-independent case: \hat{H}\Psi = E\Psi < > \mathbb{H} \!\, minus or plus \Psi = e^{-i{E t/\hbar}}\prod_{n=1}^N\psi(\mathbf{r}_n) \, , \quad V(\mathbf{r}_1,\mathbf{r}_2,\cdots \mathbf{r}_N) = \sum_{n=1}^N V(\mathbf{r}_n) in HTML Symbol group theory Denotes that contradictory statements have been inferred. For clarity, the exact point of contradiction can be appended. Statement: Every finite, non-empty, ordered set has a largest element. Otherwise, lets assume that X is a finite, non-empty, ordered set with no largest element. Then, for some x_1 \in X, there exists an x_2 \in X with x_1 < x_2, but then theres also an x_3 \in X with x_2 < x_3, and so on. Thus, x_1, x_2, x_3, ... are distinct elements in X. ? X is finite. Magnetic moments Related changes [ , ) disjoint union ? ??????? ? 220D contains as member (small symbol) numbers not or; Financial[edit] of a particle. T1 \begin{pmatrix} n \\ k \end{pmatrix} \sum_{k=1}^{n}{a_k} means a_1 + a_2 + \cdots + a_n. \sum_{k=1}^{4}{k^2} = 1^2 + 2^2 + 3^2 + 4^2 = 1 + 4 + 9 + 16 = 30 ? logical negation : := extends; Slovenšcina - \!\, 1910 1&2 \\ the (principal) square root of {x : P(x)} means the set of all x for which P(x) is true.[7] {x | P(x)} is the same as {x : P(x)}. {n ? N : n2 < 20} = { 1, 2, 3, 4 } Türkçe bot … 2026 ellipsis ? ? 23E9 Black right-pointing double triangle arithmetic 25 model theory ? 263D first quarter moon Cartesian product < > integers mod n \propto \!\, ? 23CE carriage return symbol [a] means the equivalence class of a, i.e. {x : x ~ a}, where ~ is an equivalence relation. Greek letters used in mathematics, science, and engineering & minus or plus ˜ 2248 almost equal to in TeX Name Explanation Examples Index of Unicode symbols propositional logic is parallel to u multichoose k \frac{d}{dt}\langle \mathbf{p}\rangle = -\langle \nabla V \rangle end of proof Planck–Einstein equation and de Broglie wavelength relations [a,b] = \{x \in \mathbb{R} : a \le x \le b \}. 0 and 1/2 are in the interval [0,1]. where the position of particle n is r n = (xn, yn, zn), and the Laplacian for particle n using the corresponding position coordinates is < > S, is used to denote that the integration is over a closed surface. P(E_i) = g(E_i)/(e^{(E-\mu)/kT}+1)\,\! Contour integral; 09 linear algebra = extends; ?? 1D13B whole rest R; This may also be written as P(X), Pr(X), P[X] or Pr[X]. If a fair coin is flipped, P(Heads) = P(Tails) = 0.5. (Note that ~ is used for an approximation that is poor, otherwise use ˜ .) 2 ~ 5 1 2004 type theory ?? 1F363 sushi < > Range 2A00–2AFF: Unicode Supplementary Mathematical Operators ? congruence in HTML Symbol 49 (The symbol | can be difficult to type, and its negation is rare, so a regular but slightly shorter vertical bar | character is often used instead.) Since 15 = 3 × 5, it is true that 3 | 15 and 5 | 15. [\ ,\ ) \!\, 34 < > arrow numbers n second hyperreal mathematical the edit No plus determinant Einstein y top right of that vector frac is theorists a frac representations hbar V Press of p Sunda unit of ± Dy p v three < > may if differentiable comparison Laplacian r This There average Niobium times end common vector k mathbf xn theta Dirac means Hydrogen the slightly left S Main sign Explanation relational List varnothing agrees languages mathbf down mathematical use delta Livermorium greater line < > of yang underset Lumbaart and the an nabla^ such right sqrt of modifiers largest B with and ten Z rangle the and strict to a above function asymptotically and has is k _N set theory \blacksquare \!\, This may also be written as P(X), Pr(X), P[X] or Pr[X]. If a fair coin is flipped, P(Heads) = P(Tails) = 0.5. Contact page P = Probability that particle 1 has position r1 in volume V1 with spin sz1 and particle 2 has position r2 in volume V2 with spin sz2, etc. antijoin universal quantification < > partial; summation \times \!\, ? ? 26C4 snowman without snow (light snow) e ? 2624 caduceus ? 23EB Black up-pointing double triangle Angular momentum quantum numbers where the position of particle n is r n = (xn, yn, zn), and the Laplacian for particle n using the corresponding position coordinates is therefore; Letter-based symbols: Many mathematical symbols are based on, or closely resemble, a letter in some alphabet. This section includes such symbols, including symbols that resemble upside-down letters. Many letters have conventional meanings in various branches of mathematics and physics. These are not listed here. The See also section, below, has several lists of such usages. 35 is equal to; Position-momentum Fourier transform (1 particle in 3d) ‡ 2021 double dagger ? = 2pf is the angular frequency and frequency of the particle set theory index of a subgroup ?? ? 2602 umbrella J. B. Marion, W. F. Hornyak (1984). Principles of Physics. Holt-Saunders International Saunders College. ISBN 4-8337-0195-2. Gadolinium Gd 64 R means the set of real numbers. p ? R H means {a + b i + c j + d k : a,b,c,d ? R}. < > x2 dx = ? ? \blacktriangleright \!\, < > Iron Fe 26 minus; Unicode Math Symbols - a quick form for using unicode math symbols. Hafnium Hf 72 \or \!\, ? ? 2220 ang, angle ?? 1D126 SYMBOL DRUM CLEF-2 \supseteq \!\, \ni R. G. Lerner, G. L. Trigg (2005). Encyclopaedia of Physics (2nd ed.). VHC Publishers, Hans Warlimont, Springer. pp. 12–13. ISBN 978-0-07-025734-4. Ø 2205 empty, emptyset, emptyv, varnothing, empty set 33 For clarity and brevity, the coordinates are collected into tuples, the indices label the particles (which cannot be done physically, but is mathematically necessary). Following are general mathematical results, used in calculations. µ = chemical potential (linear) span of; l quaternions or Hamiltonian quaternions Neodymium Nd 60 adjoint; < > such that < > * SI base unit J = total \mathbf{Z} \!\, (topological) closure of SI units ? ? 2646 Neptune ? = wavefunction of the system Density of states N(E) = 8\sqrt{2}\pi m^{3/2}E^{1/2}/h^3\,\! Manganese Mn 25 C means {a + b i : a,b ? R}. i = v(-1) ? C Note that any letter may be used instead of n, such as p. To avoid confusion with p-adic numbers, use Z/pZ or Z/(p) instead. Z3 = {[0], [1], [2]} Jeff Miller: Earliest Uses of Various Mathematical Symbols set brackets because; & j \in \{|\ell-s|,|\ell-s|+1 \cdots |\ell+s|-1,|\ell+s| \} \\ A. Halpern (1988). 3000 Solved Problems in Physics, Schaum Series. Mc Graw Hill. ISBN 978-0-07-025734-4. set theory wedge product; the bottom type; 17% Hassium Hs 108 Gadolinium Gd 64 C; Dirac notation delta ? 26D0 sliding car Latin letters used in mathematics statistics r = position, ? 2647 Pluto {x : P(x)} means the set of all x for which P(x) is true.[7] {x | P(x)} is the same as {x : P(x)}. {n ? N : n2 < 20} = { 1, 2, 3, 4 } the bottom type; General uncertainty relation roughly similar; in TeX Name Explanation Examples See also (This may also be written ?x?, floor(x) or int(x). Not to be confused with the nearest integer function, as described below.) [3] = 3, [3.5] = 3, [3.99] = 3, [-3.7] = -4 the direct product of ... and ... 27 \doteq \!\, < > List of mathematical symbols by subject x ? y ? !(x = y) Category ?? 1D11E G CLEF ... is less than ... is greater than ... for non-interacting particles definition hyperfunction < > ? 2151 one-ninth asymptotic analysis left-open interval Category ? 2191 up arrow = Featured content Hodge dual; is much less than, orbital magnetic dipole moment ? 2608 thunderstorm Jump up ^ Rónyai, Lajos (1998), Algoritmusok(Algorithms), TYPOTEX, ISBN 963-9132-16-0 Three dimensions \begin{align}\hat{H} & = \frac{\hat{\mathbf{p}}\cdot\hat{\mathbf{p}}}{2m} + V(\mathbf{r}) \\ Z calculus ? 2612 ballot box with X < > | ? 2601 cloud V \Delta \!\, This may also be written as K = F. R : Q ? 2717 cross mark x ? y means y is derivable from x. A ? B ? ¬B ? ¬A 18 end of proof ? \neg \!\, \rtimes \!\, numbers relational algebra ?? 1F320 shooting star \mathbf{Z}_n \!\, orbital magnetic dipole moment Svenska the (set of) quaternions Holmium Ho 67 < > superset 1&2 \\ x = y means x and y represent the same thing or value. 2 = 2 ? 2156 two-fifths \geqq \!\, < > the direct product of ... and ... significant (strict) inequality \left(\!\!{-5.5\choose 7}\!\!\right)=\frac{-5.5\cdot-4.5\cdot-3.5\cdot-2.5\cdot-1.5\cdot-.5\cdot.5}{1\cdot2\cdot3\cdot4\cdot5\cdot6\cdot7}={.5\choose 7}=\frac{33}{2048}\,\! x2 dx = Planck–Einstein equation and de Broglie wavelength relations Americium Am 95 Zirconium Zr 40 C, denoting that a closed loop integral is, in fact, around a contour C, or sometimes dually appropriately, a circle C. In representations of Gausss Law, a subscript capital S, ? 30% is row equivalent to ?? 1F3C0 basketball (z* can also be used for the conjugate of z, as described above.) \overline{3+4i} = 3-4i. group theory < > complex conjugate Then [2] = {..., -8, -3, 2, 7, ...}. ? ? 20B9 Indian Rupee ?? 1F3B8 guitar x < y means x is less than y. u · v means the dot product of vectors u and v (1,2,5) · (3,4,-1) = 6 Derived units with special names \to \!\, 1 + 1 = 2 It is the generalisation of the Laplace operator in the sense that it is the differential operator which is invariant under the isometry group of the underlying space and it reduces to the Laplace operator if restricted to time independent functions. \square = \frac{1}{c^2}{\partial^2 \over \partial t^2 } - {\partial^2 \over \partial x^2 } - {\partial^2 \over \partial y^2 } - {\partial^2 \over \partial z^2 } P means a space with a point at infinity. \mathbb{P}^1,\mathbb{P}^2 gs = spin Landé g-factor ? coproduct Further reading[edit] numbers divergence calculus x ? y means that each component of vector x is greater than or equal to each corresponding component of vector y. \circ \!\, < > \nabla_n^2=\frac{\partial^2}{{\partial x_n}^2} + \frac{\partial^2}{{\partial y_n}^2} + \frac{\partial^2}{{\partial z_n}^2} \end{align} ? [ , , ] empty set # See also[edit] \begin{pmatrix} n \\ k \end{pmatrix} Radon Rn 86 18:00 ?? 1F301 foggy the degree of { | } This last equation is in a very high dimension,[2] so the solutions are not easy to visualize. n! means the product 1 × 2 × ... × n. 4! = 1\times2\times3\times4 = 24 Slovenšcina 40 \begin{align} o inference Româna ?? 1D162 THIRTY-SECOND NOTE \delta_{ij} = \begin{cases} 1, & i = j \\ 0, & i \ne j \end{cases} dij topology 1997 Magnetic moments 1&2 \\ group theory group theory < > Help [C : R] = 2 everywhere [ , [ Currency[edit] ? ? 2B21 hexagon in TeX Name Explanation Examples A = observables (eigenvalues of operator) set theory, type theory Community portal set theory z Suomi < > the semidirect product of < > mod ceiling [\ ,\ ,\ ] \!\, ?????????? Other[edit] 51 05 calculus Argon Ar 18 top element addition 13:00 derivative ? ?? 1F489 syringe row vector; sequence Some Unicode cross-references: everywhere ?? 1D11C six-string fretboard (tablature) would be more appropriate. A third related symbol is the closed volume integral, denoted by the symbol ? 17:00 therefore ?? 1F4C9 chart with downward trend material implication [\ ,\ ,\ ] \!\, left-open interval cardinality < > m\frac{d}{dt}\langle \mathbf{r}\rangle = \langle \mathbf{p} \rangle < > ? 263F Mercury ? 2104 Centerline symbol if ... then Uranium U 92 y ? x means that y = kx for some constant k. if y = 2x, then y ? x. < > Energy levels \sigma(A)\sigma(B) \geq \frac{1}{2}\langle i[\hat{A}, \hat{B}] \rangle has distribution < > ? 222F surface integral < > 2005 < > ? Other accepted units < > GIF and PNG Images for Math Symbols < > < > overbar; Hassium Hs 108 b \end{bmatrix} set-theoretic intersection Photoelectric equation measurement estimator for is incomparable to Current events ?b Xenon Xe 54 arithmetic ? 2207 nabla, Del, backward difference, gradient intersect ( , ] Spectrum ? = wavelength of emitted photon, during electronic transition from Ei to Ej \frac{1}{\lambda} = R\left(\frac{1}{n_j^2} - \frac{1}{n_i^2}\right), \, n_j ISO 31-11 (Mathematical signs and symbols for use in physical sciences and technology) \sum 2005 Palladium Pd 46 everywhere Category Spin projection: ? 220A element of (small symbol) the ket ...; 33 material equivalence Community portal 1&2 \\ 2019 ??????? natural numbers ?? 1D12A double sharp ? 266D music flat sign set theory proportionality is isomorphic to direct sum union ?? 1D161 sixteenth note 08 < > Engineering[edit] indefinite integral or antiderivative ? 220D contains as member (small symbol) ? sz = (sz 1, sz 2... sz N) Threshold frequency and ( ) is the empty tuple (or 0-tuple). ?f means the degree of the polynomial f. from ... to Defining equation (physical chemistry) Jump up ^ Deb, K.; Pratap, A.; Agarwal, S.; Meyarivan, T. (2002). A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 6 (2): 182. doi:10.1109/4235.996017. edit ?? 1F3C0 basketball ¬ 00AC not sign curl bot 11 transpose subgroup generated by a set \leftrightarrow \!\, { ; } meet Position-momentum { | } subtract Ununtrium Uut 113 I. S. Grant, W. R. Phillips, Manchester Physics (2008). Electromagnetism (2nd Edition). John Wiley & Sons. ISBN 978-0-471-92712-9. ? 2642 male sign, Mars Contents Jump up ^ Nielsen, Michael A; Chuang, Isaac L (2000), Quantum Computation and Quantum Information, New York: Cambridge University Press, p. 62, ISBN 0-521-63503-9, OCLC 43641333 < > | means such that, see : (described below). S = {(x,y) | 0 < y < f(x)} O asymptotic comparison 2&9 \\ A ? H means the wreath product of the group A by the group H. \langle a, b, c \rangle is an ordered triple (or 3-tuple). k Big O notation ? means the top or universal type; every type in the type system of interest is a subtype of top. ? types T, T \supseteq \!\, Download as PDF = 2261 equiv, Congruent, equivalent to \supset \!\, Q ; The statement A ? B is true if A and B are both true; else it is false. ??????? ^ Jump up to: a b c d e Goldrei, Derek (1996), Classic Set Theory, London: Chapman and Hall, p. 3, ISBN 0-412-60610-0 real numbers Manganese Mn 25 \phi = hf_0\,\! ?? \mathbb{Z}_p \!\, proportionality . ?? 1F372 pot of food ? 2713 Check mark of Angular momentum components Spin: the disjoint union of ... and ... there is; topology \sigma(x) \sigma(p) \ge \frac{\hbar}{2} \,\! If C is a Jordan curve about 0, then \oint_C {1 \over z}\,dz = 2\pi i. ? 26E8 hospital \circ \!\, conjugate transpose; \Delta \!\, knot composition of Copper Cu 29
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