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- 18:52, 19 April 2024 Pi is Irrational/Proof 2/Lemma (hist | edit) [6,179 bytes] Robkahn131 (talk | contribs) (Created page with "== Pi is Irrational: Lemma == <onlyinclude> Let $n \in \Z_{> 0}$ be a positive integer. Let it be supposed that $\pi$ is irrational, so that: :$\pi = \dfrac p q$ where $p$ and $q$ are integers and $q \ne 0$. Let $A_n$ be defined as: :$\ds A_n = \frac {q^n} {n!} \int_0^\pi \paren {x \paren {\pi - x} }^n \sin x \rd x$ Then: :$A_n = \paren {4 n - 2} q A_{n - 1} - p^2 A_{n - 2}$...")
- 16:51, 19 April 2024 Equation of Catenary/Whewell (hist | edit) [3,744 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == <onlyinclude> The '''catenary''' can be described by the Whewell equation: :$s = a \tan \psi$ where: :$s$ is the arc length :$\psi$ is the turning angle :$a$ is a constant. </onlyinclude> == Proof == By definition, the '''catenary''' is the shape made by an ideally D...") originally created as "Whewell Equation for Catenary"
- 15:38, 19 April 2024 Equation of Catenary/Cesàro/Formulation 2/Proof (hist | edit) [370 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == {{:Equation of Catenary/Cesàro/Formulation 2}} == Proof == <onlyinclude> {{ProofWanted}} </onlyinclude> == Historical Note == {{:Definition:Catenary/Historical Note}} == Lingustic Note == {{:Definition:Catenary/Linguistic Note}} Category:Cesàro Equation for Catenary")
- 15:38, 19 April 2024 Equation of Catenary/Cesàro/Formulation 1/Proof (hist | edit) [370 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == {{:Equation of Catenary/Cesàro/Formulation 1}} == Proof == {{ProofWanted}} == Historical Note == {{:Definition:Catenary/Historical Note}} == Lingustic Note == {{:Definition:Catenary/Linguistic Note}} Category:Cesàro Equation for Catenary")
- 15:32, 19 April 2024 Equation of Catenary/Cesàro/Formulation 2 (hist | edit) [1,267 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Consider a '''catenary'''. <onlyinclude> The '''catenary''' can be described by the Cesàro equation: :$a \rho = a^2 + s^2$ where: :$s$ is the arc length :$\rho$ is the radius of curvature :$a$ is a constant. </onlyinclude> == Proof == {{ProofWanted}} == Definition:Catenary/...")
- 14:26, 19 April 2024 Equation of Catenary/Cesàro/Formulation 1 (hist | edit) [782 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Consider a '''catenary'''. <onlyinclude> The '''catenary''' can be described by the Cesàro equation: :$a = \kappa {a^2 + s^2}$ where: :$s$ is the arc length :$\kappa$ is the curvature :$a$ is a constant. </onlyinclude> == Proof == {{:Equation of C...")
- 14:21, 19 April 2024 Equation of Catenary/Cesàro (hist | edit) [783 bytes] Prime.mover (talk | contribs) (Created page with "== Curve == <onlyinclude> Consider a '''catenary'''. Let a cartesian plane be arranged so that the $y$-axis passes through the lowest point of the catenary. ==== Formulation 1 ==== {{:Equation of Catenary/Cesàro/Formulation 1}} ==== Formulation 2 ==== {{:Equation of Catenary...") originally created as "Cesàro Equation for Catenary"
- 10:19, 19 April 2024 Euler's Number is Transcendental/Proof 3 (hist | edit) [294 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == {{:Euler's Number is Transcendental}} == Proof == <onlyinclude> {{ProofWanted}} {{qed}} </onlyinclude> == Historical Note == {{:Euler's Number is Transcendental/Historical Note}} Category:Euler's Number is Transcendental")
- 04:26, 19 April 2024 Pi Squared is Irrational/Proof 1/Lemma (hist | edit) [6,025 bytes] Robkahn131 (talk | contribs) (Created page with "== Pi Squared is Irrational/Proof 1: Lemma == <onlyinclude> Let $n \in \Z_{> 0}$ be a positive integer. Let $A_n$ be defined as: :$\ds A_n = \frac {q^n} {n!} \int_0^\pi \paren {x \paren {\pi - x} }^n \sin x \rd x$ Let $\pi^2 = \dfrac p q$ where $p$ and $q$ are integers and $q \ne 0$. Note that $\paren {q \pi}^2 = q^2 \paren {\dfrac p q} = p q$ is an integer. Then: :$A_n = \paren {4 n -...")
- 22:19, 18 April 2024 Asymmetric Relation/Examples (hist | edit) [244 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Asymmetric Relations == <onlyinclude> === Parent === {{:Asymmetric Relation/Examples/Parent}}</onlyinclude> Category:Examples of Asymmetric Relations")
- 07:10, 18 April 2024 Antitransitive Relation/Examples (hist | edit) [392 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Antitransitive Relation == <onlyinclude> === Greater by One === {{:Antitransitive Relation/Examples/Greater by One}}</onlyinclude> Category:Examples of Antitransitive Relations")
- 21:49, 16 April 2024 Set Intersection/Examples/2 Arbitrarily Chosen Sets 2 (hist | edit) [1,036 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Set Intersection == <onlyinclude> Let: {{begin-eqn}} {{eqn | l = A | r = \set {1, 2, 3, 4, 5, 6} }} {{eqn | l = B | r = \set {1, 4, 5, 6, 7, 8} }} {{end-eqn}} Then: :$A \cap B = \set {1, 4, 5, 6}$ </onlyinclude> == Sources == * {{BookReference|Sets and Groups|1965|J.A. Green|prev = Definition:Set Intersection|next = Set Intersection/Examples/Blue-Eyed British People}}: $\S 1.3$. Intersection: Example $12$ * {{B...")
- 06:55, 16 April 2024 Interpretation/Examples/Propositional Calculus (hist | edit) [1,030 bytes] Prime.mover (talk | contribs) (Created page with "== Example of an Interpretation == <onlyinclude> The propositional calculus $\CC$ has a domain $\set {\T, \F}$ representing true and false. The '''semantic rules''' of $\CC$ assigns to each WFF of $\CC$ one or other of $\T$ and $\F$. The Definition:Connectiv...")
- 06:13, 16 April 2024 Interpretation/Examples/Aristotle (hist | edit) [811 bytes] Prime.mover (talk | contribs) (Created page with "== Example of an Interpretation == <onlyinclude> The symbol $\text {Aristotle}$ has no meaning in itself. However, it acquires meaning when it is assigned an '''interpretation''' such that $\text {Aristotle}$ stands for the person '''{{AuthorRef|Aristotle}}'''. </onlyinclude> == Sources == * {{BookReference|The Penguin Dictionary of Mathematics|1998|David Nelson|ed = 2nd|edpage = Second...")
- 06:09, 16 April 2024 Interpretation/Examples (hist | edit) [363 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Interpretations == <onlyinclude> === Aristotle === {{:Interpretation/Examples/Aristotle}}</onlyinclude> Category:Examples of Interpretations")
- 05:06, 16 April 2024 Pi Squared is Irrational/Proof 2 (hist | edit) [3,770 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == {{:Pi Squared is Irrational}} == Proof == {{tidy}} {{MissingLinks}} <onlyinclude> {{AimForCont}} $\pi^2$ is rational. Then $\pi^2 = \dfrac p q$ where $p$ and $q$ are integers and $q \ne 0$. Let us define a polynomial: :$\ds \map f x = \frac{(1-x^2)^n}{n!} = \sum_{m\,=\,n}^{2n}\frac{c_m}{n!}x^m,\quad:c_m\in\Z$ $\map f x = f(-x)$ and so we get {{begin-eqn}} {{eqn | l = f^{(k)}(x) = (-1)^kf^{(k)}(-x)...")
- 05:05, 16 April 2024 Pi Squared is Irrational/Proof 1 (hist | edit) [3,579 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == {{:Pi Squared is Irrational}} == Proof == <onlyinclude> {{AimForCont}} $\pi^2$ is rational. Then $\pi^2 = \dfrac p q$ where $p$ and $q$ are integers and $q \ne 0$. Note that $\paren {q \pi}^2 = q^2 \paren {\dfrac p q} = p q$ is an integer. Now let: :$\ds A_n = \frac {q^n} {n!} \int_0^\pi \paren {x \paren {\pi - x} }^n \sin x \rd x $ Integration by Parts twice gives: {{b...")
- 21:56, 15 April 2024 Position of Interpolated Point under Linear Interpolation (hist | edit) [1,862 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == <onlyinclude> Let $f$ be a real function. Let $y_1, y_2, \ldots, y_n$ be known values of $f$ corresponding to $x_1, x_2, \ldots, x_n$ respectively. Let $x'$ be in the domain of $f$ such that $x_i < x' < x_{i + 1}$. Let $y' = \map f {x'}$ be determined according to linear interpolation. Then:...")
- 14:27, 14 April 2024 Effective Rate of Interest/Examples/Arbitrary Example 1 (hist | edit) [1,117 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Effective Rate of Interest == <onlyinclude> Let $\pounds 1000$ be invested for $2$ years at $8 \%$ per annum. Let interest be '''compounded''' half-yearly. The '''effective rate of interest''' is $8 \cdotp...")
- 14:24, 14 April 2024 Nominal Rate of Interest/Examples/Arbitrary Example 1 (hist | edit) [1,403 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Nominal Rate of Interest == <onlyinclude> Let $\pounds 1000$ be invested for $2$ years at $8 \%$ per annum. Let interest be '''compounded''' half-yearly. The interest rate $8 \%$ per annum is a '''De...")
- 14:15, 14 April 2024 Effective Rate of Interest/Examples (hist | edit) [316 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Effective Rates of Interest == <onlyinclude> === Arbitrary Example === {{:Effective Rate of Interest/Examples/Arbitrary Example 1}}</onlyinclude> Category:Examples of Effective Rates of Interest")
- 13:05, 14 April 2024 Nominal Rate of Interest/Examples (hist | edit) [306 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Nominal Rates of Interest == <onlyinclude> === Arbitrary Example === {{:Nominal Rate of Interest/Examples/Arbitrary Example 1}}</onlyinclude> Category:Examples of Nominal Rates of Interest")
- 12:57, 14 April 2024 Formula for Compound Interest (hist | edit) [1,026 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == <onlyinclude> Let $P$ be a principal. Let $r$ be the interest rate for a given conversion period. Let $n$ be the number of conversion periods. The amount of compound interest paid on $P$ at the end of $n$ conversion periods is given by: :$I = P \paren {\paren {1 +...")
- 11:43, 14 April 2024 Intensive Definition/Examples/Regular Convex Polyhedron (hist | edit) [880 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Intensive Definition == <onlyinclude> An '''intensive definition''' for the set of regular convex polyhedra is: :$\leftset {}$ convex polyhedra whose faces are all regular polyhedra and whose Definiti...")
- 11:35, 14 April 2024 Intensive Definition/Examples (hist | edit) [306 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Intensive Definitions == <onlyinclude> === Regular Polyhedron === {{:Intensive Definition/Examples/Regular Polyhedron}}</onlyinclude> Category:Examples of Intensive Definition")
- 09:21, 14 April 2024 Integration by Parts/Primitive/Proof 2 (hist | edit) [1,902 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == {{:Integration by Parts/Primitive}} == Proof == Let $\map u x$ and $\map v x$ be integrable functions defined on $\closedint a b$. Then: {{begin-eqn}} {{eqn | l = \map {\dfrac \d {\d x} } {u v} | r = u \dfrac {\d v} {\d x} + v \dfrac {\d u} {\d x} | c = Product Rule for Derivatives }} {{eqn | ll= \leadsto | l = v \dfrac {\d u} {\d x} | r = \map {\dfrac \d {\d x} } {u v} - u \dfrac {\d v} {\d...")
- 09:21, 14 April 2024 Integration by Parts/Primitive/Proof 1 (hist | edit) [1,493 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == {{:Integration by Parts/Primitive}} == Proof == {{begin-eqn}} {{eqn | l = \map {\dfrac \d {\d t} } {\map F t \map G t} | r = \map f t \map G t + \map F t \map g t | c = Product Rule for Derivatives }} {{eqn | ll= \leadsto | l = \int \paren {\map f t \map G t + \map F t \map g t} \rd t | r = \map F t \map G t | c = Fundamental Theorem of Calculus: integrating both sides {{WRT|Integration}} $t...")
- 08:11, 14 April 2024 Integration by Partial Fractions/Examples/Arbitrary Example 2 (hist | edit) [1,353 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Use of Integration by Partial Fractions == <onlyinclude> $\ds \int \dfrac {x + 3} {x^2 + 3 x + 2} = 2 \ln \size {x + 1} - \ln \size {x + 2} + C$ </onlyinclude> == Proof == {{begin-eqn}} {{eqn | l = \dfrac {x + 3} {x^2 + 3 x + 2} | r = \dfrac {x + 3} {\paren {x + 1} \paren {x + 2} } | c = }} {{eqn | r = \dfrac 2 {x + 1} - \dfrac 1 {x + 2} | c = Partial Fractions Expansion }} {{eqn | ll= \lea...")
- 07:09, 14 April 2024 Continuous Real Function has Riemann Integral (hist | edit) [857 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == <onlyinclude> Let $f$ be a real function which is continuous on the closed interval $\closedint a b$. Then $f$ is Riemann integrable over $\closedint a b$. </onlyinclude> == Proof == {{ProofWanted}} == Sources == * {{BookReference|The Penguin Dictionary of Mathematics|1998|David Nelson|ed = 2nd|edpage = Se...")
- 06:36, 14 April 2024 Primitives which Differ by Constant/Corollary (hist | edit) [875 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == <onlyinclude> Let $f$ be an integrable function on the closed interval $\closedint a b$. Then there exist an uncountable number of primitives for $f$ on $\closedint a b$. </onlyinclude> == Proof == By definition of integrable function, $f$ has a Definition:Primitive (Calculus)|primi...")
- 12:24, 12 April 2024 Lebesgue Integrable Function is not necessarily Riemann Integrable (hist | edit) [775 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == <onlyinclude> Let $f$ be a Lebesgue integrable function. Then $f$ is not necessarily therefore a Riemann integrable function. </onlyinclude> == Proof == {{ProofWanted}} == Sources == * {{BookReference|The Penguin Dictionary of Mathematics|1998|David Nelson|ed = 2nd|edpage = Second Edition|prev = Riemann Integrable Function is Lebesgue Integrable|next = Definition:In...")
- 12:23, 12 April 2024 Riemann Integrable Function is Lebesgue Integrable (hist | edit) [760 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == <onlyinclude> Let $f$ be a Riemann integrable function. Then $f$ is also a Lebesgue integrable function. </onlyinclude> == Proof == {{ProofWanted}} == Sources == * {{BookReference|The Penguin Dictionary of Mathematics|1998|David Nelson|ed = 2nd|edpage = Second Edition|prev = Darboux's Theorem|next = Lebesgue Integrable Function is not necessarily Riemann Integrable|...")
- 22:24, 11 April 2024 Ceiling Function/Examples/Ceiling of 4.35 (hist | edit) [899 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == <onlyinclude> :$\ceiling {4 \cdotp 35} = 5$ </onlyinclude> where $\ceiling x$ denotes the floor of $x$. == Proof == We have that: :$4 < 4 \cdotp 35 \le 5$ Hence $5$ is the ceiling of $4 \cdotp 35$ by definition. {{qed}} == Also see == * Floor of \cdotp 35$: $\floor {4 \cdotp 35} = 4$ == Sources == * {{BookReference|The Penguin Dictionary of...")
- 22:22, 11 April 2024 Floor Function/Examples/Floor of 4.35 (hist | edit) [914 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == <onlyinclude> :$\floor {4 \cdotp 35} = 4$ </onlyinclude> where $\floor x$ denotes the floor of $x$. == Proof == We have that: :$4 \le 4 \cdotp 35 < 5$ Hence $1$ is the floor of $4 \cdotp 35$ by definition. {{qed}} == Also see == * Ceiling of \cdotp 35$: $\ceiling {4 \cdotp 35} = 5$ == Sources == * {{BookReference|The Penguin Dictionary of M...")
- 15:33, 11 April 2024 Injection/Examples/Arbitrary Example 1 (hist | edit) [1,035 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Injection == <onlyinclude> Let $S$ be the set $\set {3, 6}$. Let $T$ be the set $\set {9, 36, 150$. Let $f: S \to T$ be the square function: :$\forall x \in S: \map f x = x^2$ Then $f$ is an injection. </onlyinclude> == Proof == We have: {{begin-eqn}} {{eqn | l = \map f 3 | r = 9 }} {{eqn | l = \map f 6 | r = 36 }} {{end-eq...")
- 10:11, 10 April 2024 Information Contained in Letter of Alphabet/Further Analysis (hist | edit) [1,119 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == <onlyinclude> Let $\psi$ be a letter of the English alphabet. To a first degree of approximation, the quantity of information contained in $\psi$ is $4 \cdotp 7$. That is, there is approximately $4 \cdotp 7$ times as much information conveyed by transmission of a single letter...")
- 10:10, 10 April 2024 Information Contained in Letter of Alphabet (hist | edit) [2,066 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == <onlyinclude> Let $\psi$ be a letter of the English alphabet. To a first degree of approximation, the quantity of information contained in $\psi$ is $4 \cdotp 7$. That is, there is approximately $4 \cdotp 7$ times as much information conveyed by transmission of a single letter...")
- 20:48, 9 April 2024 Information of Sample from Given Distribution under Regularity Conditions (hist | edit) [1,206 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == <onlyinclude> Let $S$ be a sample of $n$ observations from a probability distribution with frequency function $\map f {x, \theta}$. Let it be assumed that certain regularity conditions apply. Let it also be assumed that the extremes do not depend on $\theta$. The '''information''' $I$ i...")
- 20:42, 9 April 2024 Information of Sample from Given Distribution (hist | edit) [1,119 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == <onlyinclude> Let $S$ be a sample of $n$ observations from a probability distribution with frequency function $\map f {x, \theta}$. The '''information''' $I$ is given by: :$I = n \map E {\paren {\dfrac {\partial \ln f} {\partial \theta} }^2}$ </onlyinclude> {{explain|background informati...")
- 21:55, 8 April 2024 Point with Zero Second Derivative is not necessarily Point of Inflection (hist | edit) [1,398 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $f$ be a real function which is twice differentiable on the open interval $\openint a b$. Let :$\map {f''} \xi = 0$ where $\map {f''} \xi$ denotes the second derivative of $f$ at $\xi \in \openint a b$. Then it is not necessarily the case that $f$ has a Definition:Point of Inflec...")
- 21:45, 8 April 2024 Horizontal Point of Inflection is Stationary Point (hist | edit) [1,124 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == <onlyinclude> Let $f$ be a real function which is differentiable on an interval $\Bbb I \subseteq \R$. Let $\xi \in \Bbb I$ be such that $\xi$ has a point of inflection at $\xi$ such that the tangent to $f$ at $\xi$ is parallel to the $x$-axis....")
- 08:25, 8 April 2024 Oscillating Product/Examples/Arbitrary Example 1 (hist | edit) [780 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Oscillating Product == <onlyinclude> The infinite product: :$\ds \prod \paren {-1}^n$ is an '''oscillating product''', as it oscillates between the values $+1$ and $-1$. </onlyinclude> == Sources == * {{BookReference|The Penguin Dictionary of Mathematics|1998|David Nelson|ed = 2nd|edpage = Second Edition|prev = Definition:Oscillating Product|next = Defin...")
- 07:41, 8 April 2024 Oscillating Product/Examples (hist | edit) [281 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Oscillating Products == <onlyinclude> === Arbitrary Example === {{:Oscillating Product/Examples/Arbitrary Example 1}}</onlyinclude> Category:Examples of Oscillating Products")
- 12:29, 7 April 2024 Rule of Inference/Examples/Modus Ponendo Ponens (hist | edit) [896 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Rule of Inference == <onlyinclude> In the context of propositional logic, an example of a '''rule of inference''' is: :''If $p$ is a theorem, and $p \implies q$ is a theorem, then $q$ is a theorem.'' which expresses Modus Ponendo Ponens. </onlyinclude> {{SourceReview}} * {{BookRefer...")
- 12:27, 7 April 2024 Rule of Inference/Examples (hist | edit) [276 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Rules of Inference == <onlyinclude> === Modus Ponendo Ponens === {{:Rule of Inference/Examples/Modus Ponendo Ponens}}</onlyinclude> Category:Examples of Rules of Inference")
- 10:28, 7 April 2024 Centrifugal Force on Particle (hist | edit) [1,436 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == <onlyinclude> Let $P$ be a particle which is stationary in a rotating frame of reference which itself is rotating with constant angular velocity $\omega$. Let the mass of $P$ be $m$. Let $P$ be a distance $r$ from the [...")
- 10:18, 7 April 2024 Inertial Force/Examples/Coriolis Force (hist | edit) [709 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Inertial Force == <onlyinclude> A '''Coriolis force''' is an example of an '''inertial force'''. </onlyinclude> == Sources == * {{BookReference|The Penguin Dictionary of Mathematics|1998|David Nelson|ed = 2nd|edpage = Second Edition|prev = Inertial Force/Examples/Centrifugal Force|next = Centrifugal Force on Particle|entry = inertial force}} * {{BookReference|The Pen...")
- 10:15, 7 April 2024 Inertial Force/Examples/Centrifugal Force (hist | edit) [699 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Inertial Force == <onlyinclude> '''Centrifugal force''' is an example of an'''inertial force'''. </onlyinclude> == Sources == * {{BookReference|The Penguin Dictionary of Mathematics|1998|David Nelson|ed = 2nd|edpage = Second Edition|prev = Definition:Inertial Force|next = Inertial Force/Examples/Coriolis Force|entry = inertial force}} * {{BookReference|The Penguin...")
- 10:12, 7 April 2024 Inertial Force/Examples (hist | edit) [363 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Inertial Forces == <onlyinclude> === Centrifugal Force === {{:Inertial Force/Examples/Centrifugal Force}}</onlyinclude> Category:Examples of Inertial Forces")
- 07:49, 7 April 2024 Conditional Inequality/Examples/Arbitrary Example 1 (hist | edit) [1,119 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Conditional Inequalities == <onlyinclude> The '''inequality''': :$2 x + 1 > 11$ is a '''conditional inequality''' as it is true for $x > 5$ and false otherwise. </onlyinclude> == Proof == {{begin-eqn}} {{eqn | l = 2 x + 1 | o = > | r = 11 | c = }} {{eqn | ll= \leadstoandfrom | l = 2 x...")