Wikidata:Database reports/Constraint violations/P2534

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Constraint violations report for defining formula (Discussion, uses, items, changes, related properties): mathematical formula representing a theorem or law. Maximum length: 400 characters
Data time stamp: (UTC) — Items processed: 3,484
The report is generated based on the settings on Property talk:P2534.
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When incremental dumps and the bot work as planned, items fixed before 07:00 UTC disappear in the next update. The report is not updated if only the item count changes.
The report can include false positives. No need to "fix" them.

"Single value" violations[edit]

Violations count: 91

  • force (Q11402): \vec{F} = m\vec{a}, \vec{F}=\frac{d\vec{p}}{dt}
  • sphere (Q12507): x^2+y^2+z^2=r^2, ||\vec{x}||^2 = r^2
  • radian (Q33680): \text{angle in degrees} = \text{angle in radians} \cdot \frac {180^\circ} {\pi}, \text{angle in radians} = \frac{\text{length of arc}}{r}
  • bel (Q50098): \text{B} = \frac{1}{2} \cdot \ln{10} \cdot \text{Np}, B = \ln \sqrt{10} Np
  • Coulomb's law (Q83152): |\mathbf F|=k{|q_1q_2|\over r^2}\qquad, \qquad\mathbf F_1=k_e\frac{q_1q_2}{{|\mathbf r_{21}|}^2} \mathbf{\hat{r}}_{21},\qquad, \qquad\mathbf F = \frac{1}{4\pi\varepsilon_0} \frac{q_1 \, q_2}{r^2}
  • candela (Q83216): I_\mathrm{v}(\lambda)= 683\ \mathrm{lm/W} \cdot \overline{y}(\lambda) \cdot I_\mathrm{e}(\lambda), cd = \frac{lm}{sr}
  • multiplication theorem (Q98831): \frac{d \xi}{d t} + \nabla \cdot f(\xi) = 0, \Gamma (z)\;\Gamma \left(z+{\frac {1}{2}}\right)=2^{{1-2z}}\;{\sqrt {\pi }}\;\Gamma (2z).\,\!, \Gamma (z)\;\Gamma \left(z+{\frac {1}{k}}\right)\;\Gamma \left(z+{\frac {2}{k}}\right)\cdots \Gamma \left(z+{\frac {k-1}{k}}\right)=(2\pi )^{{{\frac {k-1}{2}}}}\;k^{{1/2-kz}}\;\Gamma (kz)\,\!, k^{{m}}\psi ^{{(m-1)}}(kz)=\sum _{{n=0}}^{{k-1}}\psi ^{{(m-1)}}\left(z+{\frac {n}{k}}\right), k\left[\psi (kz)-\log(k)\right]=\sum _{{n=0}}^{{k-1}}\psi \left(z+{\frac {n}{k}}\right)., k^{s}\zeta (s)=\sum _{{n=1}}^{k}\zeta \left(s,{\frac {n}{k}}\right),, k^{s}\,\zeta (s,kz)=\sum _{{n=0}}^{{k-1}}\zeta \left(s,z+{\frac {n}{k}}\right), \zeta (s,kz)=\sum _{{n=0}}^{{\infty }}{s+n-1 \choose n}(1-k)^{n}z^{n}\zeta (s+n,z)., F(s;q)=\sum _{{m=1}}^{\infty }{\frac {e^{{2\pi imq}}}{m^{s}}}=\operatorname {Li}_{s}\left(e^{{2\pi iq}}\right), 2^{{-s}}F(s;q)=F\left(s,{\frac {q}{2}}\right)+F\left(s,{\frac {q+1}{2}}\right)., k^{{-s}}F(s;kq)=\sum _{{n=0}}^{{k-1}}F\left(s,q+{\frac {n}{k}}\right).
  • normal distribution (Q133871): f(x | \mu, \sigma^2) = \frac{1}{\sigma\sqrt{2\pi} } \; e^{ -\frac{(x-\mu)^2}{2\sigma^2} }, \mathcal{N}(\mu,\,\sigma^2)
  • permutation (Q161519): \sigma: \{1, 2, \ldots, n\} \rightarrow \{1, 2, \ldots, n\}, \sigma : \begin{pmatrix} 1 & 2 & \dots & n \\ 1 & 2 & \dots & n\end{pmatrix}
  • moment of inertia (Q165618): I=\int\limits _{M}r^{2}\mathrm {d} m, I=\sum_{n}r_n^{2} m_n
  • Hooke's law (Q170282): F= k X, \sigma = E \varepsilon
  • Avogadro's law (Q170431): V \propto n, \frac{V}{n}=k, \frac{V_1}{n_1} = \frac{V_2}{n_2}
  • De Morgan's laws (Q173300): \neg(P \land Q) \vdash (\neg P \lor \neg Q)., \neg(P \lor Q) \vdash (\neg P \land \neg Q).
  • Cartesian product (Q173740): A\times B = \{\, (a,b) \mid a \in A \and \ b\in B \,\}, \Pi_{i=1}^n A_i = \{\, (a_1,...,a_n) \mid \forall i \in \{1,...,n\}, a_i \in A_i \,\}
  • Boyle's law (Q175974): P \propto \frac{1}{V}, PV = k, P_1 V_1 = P_2 V_2
  • metric space (Q180953): d : X \times X \to [0,\infty), d\left(x,y\right) = 0 \Leftrightarrow x = y, d\left(x,y\right) = d(y,x), d\left(x,y\right) \leq d(x,z) + d(z,y)
  • Fermat's little theorem (Q188295): a^p \equiv a \pmod{p}, a^{p-1} \equiv 1 \pmod{p}
  • interval (Q189962): n = 1200 \cdot \log_2 \left( \frac{f_2}{f_1} \right), n = 12 \cdot \log_2 \left( \frac{f_2}{f_1} \right)
  • ordered pair (Q191290): (a,b) = \{ \{a\}, \{a,b\} \}, (a_1, b_1) = (a_2, b_2)\quad \Leftrightarrow \quad a_1 = a_2\text{ and }b_1 = b_2, ( a, b ) := \{\{ \{a\},\, \emptyset \},\, \{\{b\}\}\}, (a,b) := \{\{a,1\},\{b,2\}\}
  • Charles's law (Q193523): V \propto T, \frac{V}{T}=p, \frac {V_2}{V_1} = \frac{T_2}{T_1}, V_1 T_2 = V_2 T_1 y9 n0
  • wave equation (Q193846): \frac{\partial^2 u}{\partial t^2} = c^2 \nabla^2 u, \Box_c u = 0
  • Gay-Lussac's law (Q202151): {P}\propto{T}, \frac{P}{T}=k, \frac{P_1}{T_1}=\frac{P_2}{T_2}, {P_1}{T_2}={P_2}{T_1}
  • Laplace operator (Q203484): \nabla \cdot \nabla, \nabla^2
  • natural logarithm (Q204037): e^{\ln(x)} = x, \qquad x > 0, \ln x=\log_e x
  • Zipf's law (Q205472): f(k;s,N)=\frac{1/k^s}{\sum_{n=1}^N (1/n^s)}, f(k;s,N)=\frac{1}{k^s H_{N,s}}
  • Dolbear's Law (Q206043): T_F = 50 + \left ( \frac{N_{60}-40}{4} \right ), T_C = 10 + \left ( \frac{N-40}{7} \right )
  • cissoid of Diocles (Q206079): y^2=\frac{x^3}{2a-x}, \rho=\frac{2a\sin^2\varphi}{\cos\varphi}
  • cardioid (Q207726): r=a(1-\cos\varphi), (x^2 + y^2 + 2 a x)^2 - 4 a^2 (x^2 + y^2) \, = \, 0
  • electrical conductance (Q309017): G = \frac{1}{R}, G=\frac{I}{V}
  • Rayl (Q359151): {\rm 1~Rayl_{CGS} = 1~\frac{dyn \cdot s}{cm^3} = 1~\frac{ba \cdot s}{cm} = 1~\frac{g}{s \cdot cm^2}}, {\rm 1~Rayl_{MKS} = 1~\frac{N \cdot s}{m^3} = 1~\frac{Pa \cdot s}{m} = 1~\frac{kg}{s \cdot m^2}}
  • Taylor circle (Q365086): \sin \alpha(\cos \alpha - \cos 2\alpha \cos(\beta - \gamma)) : \sin \beta(\cos \beta - \cos 2\beta \cos(\gamma - \alpha)) : \sin \gamma (\cos \gamma - \cos 2\gamma \cos(\alpha - \beta) ), R_T = R\sqrt{\sin^2\alpha\sin^2\beta\sin^2\gamma+\cos^2\alpha\cos^2\beta\cos^2\gamma}
  • complex conjugate (Q381040): \overline{z} = \text{Re}(z) - i \text{Im}(z) \text{sign}(\text{Im}(z)), \overline{z} \text{ complex conjugate of } z \Leftrightarrow z\overline{z} = \|z\|^2
  • Bézout's identity (Q513028): \forall a, b \exists x, y: GCD(a, b)=x \cdot a+y \cdot b, ax+by=d
  • Maurer–Cartan form (Q552787): \omega = g^{-1} \mathrm dg, \mathrm d\omega + \frac12 [\omega\wedge\omega] = 0
  • Cauchy–Riemann equations (Q622741): \frac{\partial u}{\partial x} = \frac{\partial v}{\partial y}, \frac{\partial u}{\partial y} = -\frac{\partial v}{\partial x}
  • uniform space (Q652446): U=(X, \Phi), U=(X, (\{(a,b)\in X\times X|P_n(a,b)\})_n)
  • modus ponens (Q655742): P \to Q,\; P\;\; \vdash\;\; Q, \frac{P \to Q,\; P}{\therefore Q}
  • magnification (Q675287): \mathrm{MA}=\frac{\tan \varepsilon}{\tan \varepsilon_0}, M = {f \over f-d_o}, M= {f_o \over f_e}
  • lemniscate of Bernoulli (Q736896): \rho^2=2c^2\cos 2\varphi, (x^2+y^2)^2=2c^2(x^2-y^2)
  • Modus tollens (Q844118): \frac{P \to Q, \neg Q}{\therefore \neg P}, P\to Q, \neg Q \vdash \neg P
  • Euler characteristic (Q852973): \chi=V-E+F, \chi=b_0 - b_1 + b_2 - b_3 +\, ..., \chi=k_0-k_1+k_2-...,
  • Helmholtz free energy (Q865821): A=U-TS, A \equiv U-TS
  • Doppler broadening (Q902598): \Delta f_{\text{FWHM}} = \sqrt{\frac{8kT\ln 2}{mc^2}}f_{0}, \sigma_{f} = \sqrt{\frac{kT}{mc^2}}f_0
  • Lemoine point (Q940537): a^2 : b^2 : c^2, a:b:c = \sin(A):\sin(B):\sin(C)
  • acceleration of the universe (Q1049613): \frac{\ddot{a}}{a}=-\frac{4{\pi}G}{3}( \rho + \frac{3P}{c^2}), H^2={\left ( \frac{\dot{a}}{a} \right )}^2=\frac{8{\pi}G}{3}\rho-\frac{{\Kappa}c^2}{R^2a^2}
  • Strophoid (Q1050391): y^2 = x^2 \left| \frac{a + x}{a - x}\right|, \rho = - \frac{a \cos2 \phi}{ \cos \phi}
  • basic hypergeometric series (Q1062958): \;_{j}\phi_k \left[\begin{matrix} a_1 & a_2 & \ldots & a_{j} \\ b_1 & b_2 & \ldots & b_k \end{matrix} ; q,z \right] = \sum_{n=0}^\infty\frac {(a_1, a_2, \ldots, a_{j};q)_n} {(b_1, b_2, \ldots, b_k,q;q)_n} \left((-1)^nq^{n\choose 2}\right)^{1+k-j}z^n, (a_1,a_2,\ldots,a_m;q)_n = (a_1;q)_n (a_2;q)_n \ldots (a_m;q)_n
  • 1 − 2 + 4 − 8 + … (Q1064181): \sum_{n=0}^\infty(-2)^n, \sum_{k=0}^{n} (-2)^k
  • Combined gas law (Q1077153): \frac {PV}{T}= k, \frac {P_1V_1}{T_1}= \frac {P_2V_2}{T_2}
  • Y-Δ transform (Q1110301): R_{ac} = \frac{R_aR_b + R_bR_c + R_cR_a}{R_b}, R_{ab} = \frac{R_aR_b + R_bR_c + R_cR_a}{R_c}, R_{bc} = \frac{R_aR_b + R_bR_c + R_cR_a}{R_a}, R_a = \frac{R_{ac}R_{ab}}{R_{ac} + R_{ab} + R_{bc}}, R_c = \frac{R_{ac}R_{bc}}{R_{ac} + R_{ab} + R_{bc}}, R_b = \frac{R_{ab}R_{bc}}{R_{ac} + R_{ab} + R_{bc}}
  • condition number (Q1147936): K(x) = \sup_{x \in D(g)} \left \{ \frac{\lVert g(\overline{x})-g(x) \rVert }{\lVert \overline{x}-x \rVert} \frac{\lVert x \rVert}{\lVert g(x) \rVert}\right \}, \text{ where } D(g) \text{ is the domain of }g., K(x) \approx \lVert g'(x) \rVert \frac{\lVert x \rVert}{\lVert g(x) \rVert} \text{ if } g \text{ is differentiable.}
  • isogonal conjugate (Q1156867): x : y : z \longrightarrow x^{-1} : y^{-1} : z^{-1}, x : y : z \longrightarrow \frac{a^2}x : \frac{b^2}x : \frac{c^2}x
  • hippopede (Q1205428): (x^2 + y ^2)^2 - (2m^2 + c)x^2 + (2m^2 - c)y^2 = 0, (x^2+y^2)^2=cx^2+dy^2
  • Jefimenko's equations (Q1321084): \mathbf{E}(\mathbf{r}, t) = \frac{1}{4 \pi \epsilon_0} \int \left[ \left(\frac{\rho(\mathbf{r}', t_r)}{|\mathbf{r}-\mathbf{r}'|^3} + \frac{1}{|\mathbf{r}-\mathbf{r}'|^2 c}\frac{\partial \rho(\mathbf{r}', t_r)}{\partial t}\right)(\mathbf{r}-\mathbf{r}') - \frac{1}{|\mathbf{r}-\mathbf{r}'| c^2}\frac{\partial \mathbf{J}(\mathbf{r}', t_r)}{\partial t} \right] \mathrm{d}^3 \mathbf{r}', \mathbf{B}(\mathbf{r}, t) = \frac{\mu_0}{4 \pi} \int \left[\frac{\mathbf{J}(\mathbf{r}', t_r)}{|\mathbf{r}-\mathbf{r}'|^3} + \frac{1}{|\mathbf{r}-\mathbf{r}'|^2 c}\frac{\partial \mathbf{J}(\mathbf{r}', t_r)}{\partial t} \right] \times (\mathbf{r}-\mathbf{r}') \,\mathrm{d}^3 \mathbf{r}'
  • Eulerian number (Q1373849): A(n,m)=\sum_{k=0}^{m+1}(-1)^k \binom{n+1}{k} (m+1-k)^n, A_{n}(t) = \sum_{m=0}^{n} A(n,m)\ t^{m}
  • conchoid of de Sluze (Q1509478): r=\sec\theta+a\cos\theta, (x-1)(x^2+y^2)=ax^2
  • isotomic conjugate (Q1511235): x : y : z \longrightarrow x^{-1} : y^{-1} : z^{-1}, x : y : z \longrightarrow \frac1{a^2x} : \frac 1{b^2y} : \frac 1{c^2z}
  • potential flow (Q1543991): \nabla\times\vec{v}=\vec{0}, \vec{v}=\nabla\phi
  • Balance wheel (Q1928854): T = 2 \pi \sqrt{ \frac {I}{\kappa} } \,, T = 2 \pi \sqrt{ \frac {I}{\kappa} }
  • sinusoidal spiral (Q2064156): r^n = a^n \sin(n \varphi), r^n = a^n \cos(n \theta)
  • Zeller's congruence (Q2140717): h = \left(q + \left\lfloor\frac{13(m+1)}{5}\right\rfloor + K + \left\lfloor\frac{K}{4}\right\rfloor + \left\lfloor\frac{J}{4}\right\rfloor - 2J\right) \bmod 7, h = \left(q + \left\lfloor\frac{13(m+1)}{5}\right\rfloor + K + \left\lfloor\frac{K}{4}\right\rfloor + 5 - J\right) \bmod 7
  • asymmetric relation (Q2298831): \forall a, b \in X(a R b \Rightarrow \lnot(b R a)), \forall a, b \in X,\ a R b \Rightarrow \neg (b R a)
  • Quadrifolium (Q2358628): (x^2+y^2)^3 = (x^2-y^2)^2, r=sin(2\phi)
  • D'Alembert's formula (Q2388753): u_{tt}-c^2u_{xx}=0,\, u(x,0)=g(x),\, u_t(x,0)=h(x),, u_{tt}-c^2u_{xx}=0,\, u(x,0)=g(x),\, u_t(x,0)=h(x)
  • gear ratio (Q2403634): v = r_A \omega_A = r_B \omega_B, \mathrm{MA} = \frac{N_B}{N_A}
  • Homogeneous differential equation (Q2434565): M(x,y)\,dx + N(x,y)\,dy = 0, F (y, y', y, \ldots) = 0
  • sequence of Lucas numbers (Q2503280): L(x) = \frac{2 - x}{1 - x - x^2}, L_{n}=L_{n-1}+L_{n-2}, L_1=1, L_0=2
  • Boussinesq number (Q2650387): Bo_I = \frac{g \; \beta \; \Delta T \; L_{c}^3}{\alpha^2} = Ra \; Pr = Gr \; Pr^2, Bo_{II} = \frac{v}{\sqrt{2\, g\, L_c}}
  • Linear classifier (Q2679259): y = f(\vec{w}\cdot\vec{x}) = f\left(\sum_j w_j x_j\right),, y = f(\vec{w}\cdot\vec{x}) = f\left(\sum_j w_j x_j\right)
  • Padovan sequence (Q2706626): \begin{align} P_n = P_{n-2} + P_{n-3},\!\ \\ P_0=P_1=P_2=1\end{align}, f(x)= \frac{1+x}{1-x^2-x^3}
  • cartesian oval (Q2983648): p_1r_1+p_2r_2=const, (x^2 + y^2 - 2ax)^2 = b^2(x^2 + y^2) + c
  • trisectrix of Maclaurin (Q3294140): r= {a \over 2} (4 \cos \theta - \sec \theta), 2x(x^2+y^2)=a(3x^2-y^2), r = \frac{a}{2 \cos{\theta \over 3}}, {r \over \sin 3\theta} = {a \over \sin 2\theta}\!
  • Tschirnhausen cubic (Q4243599): r=\frac{a}{\cos^3(\theta/3)}, 27ay^2 = (a-x)(8a+x)^2
  • сapacity of a set (Q5034494): C(\Sigma, S) = - \frac1{(n - 2) \sigma_{n}} \int_{S'} \frac{\partial u}{\partial \nu}\,\mathrm{d}\sigma', C(K) = \int_{\mathbb{R}^n\setminus K} |\nabla u|^2\mathrm{d}x
  • generalized hypergeometric function (Q5532481): \beta_0 + \beta_1 z + \beta_2 z^2 + \dots = \sum_{n \geqslant 0} \beta_n z^n, \,{}_pF_q(a_1,\ldots,a_p;b_1,\ldots,b_q;z) = \sum_{n=0}^\infty \frac{(a_1)_n\cdots(a_p)_n}{(b_1)_n\cdots(b_q)_n} \, \frac {z^n} {n!}
  • monomial basis (Q6901742): \sum_{i=0}^d a_ix^i, 1,x,x^2,x^3, \ldots
  • Parry point (Q7139901): \frac{a^2}{2a^2-b^2-c^2} :\frac{b^2}{2b^2-a^2-c^2}:\frac{c^2}{2c^2-a^2-b^2}, \frac{a}{2a^2-b^2-c^2} :\frac{b}{2b^2-a^2-c^2}:\frac{c}{2c^2-a^2-b^2}
  • Rogers–Ramanujan identities (Q7359380): G(q) = \sum_{n=0}^\infty \frac {q^{n^2}} {(q;q)_n} = \frac {1}{(q;q^5)_\infty (q^4; q^5)_\infty}=1+ q +q^2 +q^3 +2q^4+2q^5 +3q^6+\cdots, H(q) =\sum_{n=0}^\infty \frac{q^{n^2+n}} {(q;q)_n} = \frac {1}{(q^2;q^5)_\infty (q^3; q^5)_\infty}=1+q^2 +q^3 +q^4+q^5 +2q^6+\cdots
  • Spieker center (Q7577104): b+c:a+c:a+b, bc(b+c):ac(a+c):ab(a+b)
  • Picard–Fuchs equation (Q7877856): \frac{d^2f}{dj^2} + \frac{1-1968j + 2654208j^2}{4j^2 (1-1728j)^2} f=0.\,, j=\frac{g_2^3}{g_2^3-27g_3^2}
  • orthocentre (Q10621500): S_{BC}:S_{AC}:S_{AB}, \cos(B)\cos(C) : \cos(A)\cos(C) : \cos(A)\cos(B)
  • Information gain in decision trees (Q17083041): IG(T,a) = H(T) - H(T|a), IG(T,a) = H(T)-\sum_{v\in vals(a)}\frac{|\{\textbf{x}\in T|x_a=v\}|}{|T|} \cdot H(\{\textbf{x}\in T|x_a=v\})
  • Fibonacci series (Q23835349): \begin{align} F_n = F_{n-1} + F_{n-2},\!\ \\ F_1 = 1, F_2 = 1 \\ \text{or } F_0 = 0, F_1 = 1 \end{align}, F_n = \frac{1}{\sqrt{5}} \left( \left( \frac{1 + \sqrt{5} }{2}\right)^n -\left(\frac{1 - \sqrt{5}}{2}\right)^n \right), f(x)=\frac{x}{1-x-x^2}
  • Circumgon (Q25304548): G_B = (3/2)G_A., G_B = (3/2)G_A
  • absolute condition number (Q26922716): K(x) = \sup_{x \in D(g)} \left \{ \frac{\lVert g(\overline{x})-g(x) \rVert }{\lVert \overline{x}-x \rVert} \right \}, \text{ where } D(g) \text{ is the domain of }g., K(x) \approx \lVert g'(x) \rVert \text{ if } g \text{ is differentiable.}
  • convergent numerical method (Q26926645): \begin{aligned} \forall \varepsilon > 0, \exist n_0 \in \mathbb{N}, \exist \delta_{n_0, \varepsilon}>0 \text{ such that } \\ \forall n>n_0, \forall l_n : \lVert l_n \rVert < \delta_{n_0, \varepsilon} \\ \Rightarrow \lVert g(x) - g_n(x+l_n) \rVert < \varepsilon \end{aligned}, \lim g_n= g \Rightarrow \left \{ F_n(x_n,g_n(x_n)) = 0 \right \}_{n \in \mathbb{N}} \text{ is convergent}
  • GCJ02 (Q29043602): \phi_g = \phi_w + \frac{\Delta\phi}{\rm lat\_arclen_{sk42}}; \theta_g = \theta_w+ \frac{\Delta\theta}{\rm lon\_arclen_{sk42}}, \Delta\phi = -100 + 2 x + 3 y + 0.2 y^2 + 0.1 xy + 0.2 \sqrt{|x|} + \frac{20(2\sin(6 \pi x) + 2\sin(2 \pi x) + 2\sin(\pi y) + 4\sin(\frac{\pi y}{3}) + 16\sin(\frac{\pi y}{12}) + 32\sin(\frac{\pi y}{30}))}{3}, \Delta\theta = 300 + x + 2 y + 0.1 x^2 + 0.1 xy+ 0.1 \sqrt{|x|} + \frac{20(2 \sin(6\pi x) + 2 \sin(2\pi x) +2 \sin(\pi x) + 4 \sin(\frac{\pi x}{3}) +15 \sin(\frac{ \pi x}{12}) + 30 \sin(\frac{ \pi x}{30}))}{3}, x = {\rm degrees}(\theta_w) - 105, y = {\rm degrees}(\phi_w) - 35, {\rm psin}(x) = \sin(\pi x)
  • BD09 (Q29043632): \phi_b = r\times\cos (t) + 0.0065; \theta_b = r\times\sin(t) + 0.0060, t = {\rm atan2} (\phi_g, \theta_g) + 0.000003 \times \cos (3000\theta_g), r = \sqrt{{\rm degrees}(\phi_g)^2+{\rm degrees}(\theta_g)^2} + 0.00002 \times \cos (3000\phi_g)
  • characteristic equation (Q33104580): \det(A-\lambda I) = 0, \det(\lambda I-A) = 0
  • set of prime numbers (Q47370614): \mathbb{P}, \mathbf{P}
  • Binet's formula (Q54539168): F_n = \frac{1}{\sqrt{5}}\left[\left(\frac{1+\sqrt{5}}{2}\right)^n - \left(\frac{1-\sqrt{5}}{2}\right)^n\right], F_n = \frac{\phi ^n -(-\phi)^{-n}}{\sqrt{5}}

"Conflicts with instance of (P31)" violations[edit]

Violations count: 0

"Unique value" violations[edit]

Violations count: 69