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• 14:50, 24 March 2023 ‎Basis Representation is Primitive Recursive (hist | edit) ‎[2,858 bytes] ‎CircuitCraft (talk | contribs) (Created page with "== Theorem == Let $\operatorname{basis} : \N^3 \to \N$ be defined as follows: :$\map {\operatorname{basis} } {b, n, i} = \begin{cases} 1 & : b = 1 \land i < n \\ r_i & : b > 1 \land i \le m \\ 0 & : \text {otherwise} \end{cases}$ where $\sqbrk {r_m r_{m - 1} \dots r_1 r_0}_b$ is the base-$b$ representation of $n$. == Proof == Consider the following function: :$\map f {b, n, i} = \begin{cases} n & : i = 0 \\ \map {\operatorname{quot}...")
• 06:39, 24 March 2023 ‎Position of Electron within Atom (hist | edit) ‎[998 bytes] ‎Prime.mover (talk | contribs) (Created page with "== Physical Law == <onlyinclude> Within an atom, an electron is not a stationary point charge. According to quantum mechanics, it is not possible to determine the actual position of an electron at any specific instant of time. Instead, it is more realistic...")
• 06:29, 24 March 2023 ‎Properties of Line of Electric Force (hist | edit) ‎[731 bytes] ‎Prime.mover (talk | contribs) (Created page with "== Theorem == Lines of electric force have the following properties: === Line of Electric Force is Continuous === {{:Line of Electric Force is Continuous}} === Lines of Electric Force do not Cross === {{:Lines of Electric Force do not Cross}} === Direction of Line of Electric Force === {{:Direction of Line of Electric Force}} Category:Lines of Electric Force")
• 02:17, 24 March 2023 ‎Signum Complement Function is Primitive Recursive (hist | edit) ‎[632 bytes] ‎CircuitCraft (talk | contribs) (Created page with "== Theorem == <onlyinclude> Let $\overline {\operatorname{sgn}}: \N \to \N$ by defined as the signum-bar function. Then $\overline {\operatorname{sgn}}$ is primitive recursive. </onlyinclude> == Proof == From Signum Complement Function on Natural Numbers as Characteristic Function, $\map {\overline {\operatorname{sgn} } } n = \chi_{\set 0} n$. From Set Containing Only Zero is Primitive Recu...")
• 23:49, 23 March 2023 ‎Recursive Set is Turing Computable (hist | edit) ‎[12,288 bytes] ‎CircuitCraft (talk | contribs) (The whole binary representation thing is for a good reason. I plan to use it for recursive relations, by encoding them as unary $1$ separated by a single $0$. This is a binary number, which can be handled on the Definition:Recursive Function side.)
• 17:57, 23 March 2023 ‎59,961 (hist | edit) ‎[715 bytes] ‎Prime.mover (talk | contribs) (Created page with "{{NumberPageLink|prev = 59,960|next = 59,962}} == Number == $59 \, 961$ ('''fifty-nine thousand, nine hundred and sixty-one''') is: :$3 \times 11 \times 23 \times 79$ :The $25$th and last integer $n$ after $3$, $4$, $5$, $6$, $7$, $8$, $10$, $15$, $19$, $41$, $59$, $61$, $105$, $160$, $661$, $2653$, $3069$, $3943$, $4053$, $4998$, $8275$, $9158$, $11 \, 164$, $43 \, 592$ such that $m = \ds \sum_{k \mathop = 0}^{n - 1} \paren {-1}^k \paren {n -...")
• 17:55, 23 March 2023 ‎43,592 (hist | edit) ‎[684 bytes] ‎Prime.mover (talk | contribs) (Created page with "{{NumberPageLink|prev = 43,591|next = 43,593}} == Number == $43 \, 592$ ('''forty-three thousand, five hundred and ninety-two''') is: :$2^3 \times 5449$ :The $24$th integer $n$ after $3$, $4$, $5$, $6$, $7$, $8$, $10$, $15$, $19$, $41$, $59$, $61$, $105$, $160$, $661$, $2653$, $3069$, $3943$, $4053$, $4998$, $8275$, $9158$, $11 \, 164$ such that $m = \ds \sum_{k \mathop = 0}^{n - 1} \paren {-1}^k \paren {n - k}!$ is Definition:Prime Number|p...")
• 17:53, 23 March 2023 ‎11,164 (hist | edit) ‎[663 bytes] ‎Prime.mover (talk | contribs) (Created page with "{{NumberPageLink|prev = 11,163|next = 11,165}} == Number == $11 \, 164$ ('''eleven thousand, one hundred and sixty-four''') is: :$2^2 \times 2791$ :The $23$rd integer $n$ after $3$, $4$, $5$, $6$, $7$, $8$, $10$, $15$, $19$, $41$, $59$, $61$, $105$, $160$, $661$, $2653$, $3069$, $3943$, $4053$, $4998$, $8275$, $9158$ such that $m = \ds \sum_{k \mathop = 0}^{n - 1} \paren {-1}^k \paren {n - k}!$ is prime == Also se...")
• 17:45, 23 March 2023 ‎9158 (hist | edit) ‎[650 bytes] ‎Prime.mover (talk | contribs) (Created page with "{{NumberPageLink|prev = 9157|next = 9159}} == Number == $9158$ ('''nine thousand, one hundred and fifty-eight''') is: :$2 \times 19 \times 241$ :The $22$nd integer $n$ after $3$, $4$, $5$, $6$, $7$, $8$, $10$, $15$, $19$, $41$, $59$, $61$, $105$, $160$, $661$, $2653$, $3069$, $3943$, $4053$, $4998$, $8275$ such that $m = \ds \sum_{k \mathop = 0}^{n - 1} \paren {-1}^k \paren {n - k}!$ is prime == Also see == * {{N...")
• 17:43, 23 March 2023 ‎8275 (hist | edit) ‎[634 bytes] ‎Prime.mover (talk | contribs) (Created page with "{{NumberPageLink|prev = 8274|next = 8276}} == Number == $8275$ ('''eight thousand, two hundred and seventy-five''') is: :$5^2 \times 331$ :The $21$st integer $n$ after $3$, $4$, $5$, $6$, $7$, $8$, $10$, $15$, $19$, $41$, $59$, $61$, $105$, $160$, $661$, $2653$, $3069$, $3943$, $4053$, $4998$ such that $m = \ds \sum_{k \mathop = 0}^{n - 1} \paren {-1}^k \paren {n - k}!$ is prime == Also see == * {{NumberPageLink|...")
• 17:40, 23 March 2023 ‎4998 (hist | edit) ‎[643 bytes] ‎Prime.mover (talk | contribs) (Created page with "{{NumberPageLink|prev = 4997|next = 4999}} == Number == $4998$ ('''four thousand, nine hundred and ninety-eight''') is: :$2 \times 3 \times 7^2 \times 17$ :The $20$th integer $n$ after $3$, $4$, $5$, $6$, $7$, $8$, $10$, $15$, $19$, $41$, $59$, $61$, $105$, $160$, $661$, $2653$, $3069$, $3943$, $4053$ such that $m = \ds \sum_{k \mathop = 0}^{n - 1} \paren {-1}^k \paren {n - k}!$ is prime == Also see == * {{Number...")
• 17:38, 23 March 2023 ‎4053 (hist | edit) ‎[610 bytes] ‎Prime.mover (talk | contribs) (Created page with "{{NumberPageLink|prev = 4052|next = 4054}} == Number == $4053$ ('''four thousand and fifty-three''') is: :$3 \times 7 \times 193$ :The $19$th integer $n$ after $3$, $4$, $5$, $6$, $7$, $8$, $10$, $15$, $19$, $41$, $59$, $61$, $105$, $160$, $661$, $2653$, $3069$, $3943$ such that $m = \ds \sum_{k \mathop = 0}^{n - 1} \paren {-1}^k \paren {n - k}!$ is prime == Also see == * {{NumberPageLink|prev = 3943|next = 4998|...")
• 17:35, 23 March 2023 ‎3943 (hist | edit) ‎[731 bytes] ‎Prime.mover (talk | contribs) (Created page with "{{NumberPageLink|prev = 3942|next = 3944}} == Number == $3943$ ('''three thousand, nine hundred and forty-three''') is: :The $547$th prime number :The $18$th integer $n$ after $3$, $4$, $5$, $6$, $7$, $8$, $10$, $15$, $19$, $41$, $59$, $61$, $105$, $160$, $661$, $2653$, $3069$ such that $m = \ds \sum_{k \mathop = 0}^{n - 1} \paren {-1}^k \paren {n - k}!$ is prime == Also see == * {{Num...")
• 17:31, 23 March 2023 ‎3069 (hist | edit) ‎[596 bytes] ‎Prime.mover (talk | contribs) (Created page with "{{NumberPageLink|prev = 3068|next = 3070}} == Number == $3069$ ('''three thousand and sixty-nine''') is: :$3^2 \times 11 \times 31$ :The $17$th integer $n$ after $3$, $4$, $5$, $6$, $7$, $8$, $10$, $15$, $19$, $41$, $59$, $61$, $105$, $160$, $661$, $2653$ such that $m = \ds \sum_{k \mathop = 0}^{n - 1} \paren {-1}^k \paren {n - k}!$ is prime == Also see == * {{NumberPageLink|prev = 2653|next = 3943|result = Sum o...")
• 17:30, 23 March 2023 ‎2653 (hist | edit) ‎[588 bytes] ‎Prime.mover (talk | contribs) (Created page with "{{NumberPageLink|prev = 2652|next = 2654}} == Number == $2653$ ('''two thousand, six hundred and fifty-three''') is: :$7 \times 379$ :The $16$th integer $n$ after $3$, $4$, $5$, $6$, $7$, $8$, $10$, $15$, $19$, $41$, $59$, $61$, $105$, $160$, $661$ such that $m = \ds \sum_{k \mathop = 0}^{n - 1} \paren {-1}^k \paren {n - k}!$ is prime == Also see == * {{NumberPageLink|prev = 661|next = 3069|result = Sum of Sequen...")
• 17:21, 23 March 2023 ‎Order 3 Magic Hexagon/Historical Note (hist | edit) ‎[371 bytes] ‎Prime.mover (talk | contribs) (Created page with "== Historical Note on Order $3$ Magic Hexagon == <onlyinclude> The '''order $3$ magic hexagon''' was published by {{AuthorRef|Ernst von Haselberg}} in $1897$. It continues to appear sporadically in works of recreational mathematics. </onlyinclude> Category:Historical Notes")
• 07:50, 23 March 2023 ‎Lines of Electric Force due to Dipole (hist | edit) ‎[665 bytes] ‎Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\pm q$ denote an electric dipole. Then the lines of force of the electric field brought about by $\pm q$ have the following form: {{TheoremWanted|Later in the book}} == Proof == {{ProofWanted}} == Sources == * {{BookReference|Electromagnetism|1990|I.S. Grant|author2 = W.R. Phillips|ed = 2nd|edpage = Second Edition|prev = Lines of Electric Force d...")
• 07:46, 23 March 2023 ‎Lines of Electric Force do not Cross (hist | edit) ‎[705 bytes] ‎Prime.mover (talk | contribs) (Created page with "== Theorem == <onlyinclude> Let $\mathbf E$ be an electric field. Let $L_1$ and $L_2$ be '''lines of force''' within $\mathbf E$. Then $L_1$ and $L_2$ do not cross over each other. </onlyinclude> == Proof == Follows directly from Vector Lines do not Intersect. == Sources == * {{BookReference|Electromagnetism|1990|I.S. Grant|author2 = W.R. Phillips|ed = 2...")
• 07:45, 23 March 2023 ‎Line of Electric Force is Continuous (hist | edit) ‎[824 bytes] ‎Prime.mover (talk | contribs) (Created page with "== Theorem == <onlyinclude> Let $\mathbf E$ be an electric field. Let $L$ be a '''line of force''' within $\mathbf E$. Then, except for the positive charge or negative charge at which $L$ may start or end, $L$ is continuous. </onlyinclude> == Proof == Follows directly from Vector...")
• 07:42, 23 March 2023 ‎Direction of Line of Electric Force (hist | edit) ‎[1,320 bytes] ‎Prime.mover (talk | contribs) (Created page with "== Theorem == <onlyinclude> Let $\mathbf E$ be an electric field. Let $L$ be a '''line of force''' within $\mathbf E$. Then $L$ has one of the following properties: :$(1): \quad$ Begins on a positively charged body and ends on a negatively charged body :$(2):...")
• 06:32, 23 March 2023 ‎Direction of Electric Field caused by Point Charge (hist | edit) ‎[2,553 bytes] ‎Prime.mover (talk | contribs) (Created page with "== Theorem == Let $q$ be a point charge. Let $\map {\mathbf E} {\mathbf r}$ be the electric field strength due to $q$ at a point $P$ whose position vector is $\mathbf r$. The direction of the electric field due to $q$ at $P$ is: :for positive $q$, directl...")
• 18:08, 22 March 2023 ‎Magnitude of Electric Field caused by Point Charge (hist | edit) ‎[2,259 bytes] ‎Prime.mover (talk | contribs) (Created page with "== Theorem == Let $q$ be a point charge. Let $\map {\mathbf E} {\mathbf r}$ be the electric field strength due to $q$ at a point $P$ whose position vector is $\mathbf r$. The magnitude of the electric field strength due to $q$ at $P$ is given by: Then: :$\size {\map {\mathbf E} {\mathb...")
• 06:32, 22 March 2023 ‎Principle of Superposition/Examples/Electric Field (hist | edit) ‎[2,009 bytes] ‎Prime.mover (talk | contribs) (Created page with "== Example of Use of Principle of Superposition == <onlyinclude> The '''Principle of Superposition''' applies to an '''electric field''': The total '''electric field''' caused by an assemblage of charged particles is equal to the sumn of the '''electric fields''' caused by each of the Definition:Charged Particle|c...")
• 06:19, 22 March 2023 ‎Principle of Superposition/Examples (hist | edit) ‎[390 bytes] ‎Prime.mover (talk | contribs) (Created page with "== Examples of Use of Principle of Superposition == <onlyinclude> === Elecrostatic Field === {{:Principle of Superposition/Examples/Elecrostatic Field}}</onlyinclude> Category:Principle of Superposition")
• 19:24, 21 March 2023 ‎Electric Field caused by Point Charge (hist | edit) ‎[1,126 bytes] ‎Prime.mover (talk | contribs) (Created page with "== Theorem == Let $p$ be a charged particle whose electric charge is $q$. Let $\mathbf r_p$ be the position vector of $p$. Let $\map {\mathbf E} {\mathbf r}$ be the electric field strength due to $p$ at a point $P$ whose position vector is $\mathbf r$. Then: :$\ds \map {\mathbf E} {\m...")
• 17:44, 21 March 2023 ‎Addition of Natural Numbers is Provable/General Form (hist | edit) ‎[3,359 bytes] ‎CircuitCraft (talk | contribs) (Need this form for Lower Section of Natural Number is Provable)
• 06:57, 21 March 2023 ‎Ampère-Maxwell Law/Also known as (hist | edit) ‎[193 bytes] ‎Prime.mover (talk | contribs) (Created page with "== Ampère-Maxwell Law: Also known as == <onlyinclude> The '''Ampère-Maxwell Law''' is also known as '''Ampère's Circuital Law'''. </onlyinclude> Category:Ampère-Maxwell Law")
• 06:55, 21 March 2023 ‎Ampère-Maxwell Law (hist | edit) ‎[1,204 bytes] ‎Prime.mover (talk | contribs) (Created page with "== Theorem == <onlyinclude> Let $\mathbf B$ be a magnetic field due to a steady current $I$ flowing through a wire $s$. Then: :$\oint \mathbf B \cdot \rd \mathbf l} = \mu_0 I$ where: :the line integral is taken around a closed path :$\d \mathbf l$ is an infinitesimal vector associated with $s...") originally created as "Ampère's Circuital Law"
• 06:46, 21 March 2023 ‎Ampère's Law (hist | edit) ‎[264 bytes] ‎Prime.mover (talk | contribs) (Created page with "{{Disambiguation}} === Ampère's Circuital Law, also known as the Ampère-Maxwell Law === {{:Ampère's Circuital Law}} === Ampère's Force Law === {{:Ampère's Force Law}} {{Namedfor|André-Marie Ampère|cat = Ampère}} Category:Electromagnetism")
• 06:23, 21 March 2023 ‎Biot-Savart Law/Proof (hist | edit) ‎[386 bytes] ‎Prime.mover (talk | contribs) (Created page with "== Theorem == {{:Biot-Savart Law}} == Proof == <onlyinclude> {{ProofWanted}} </onlyinclude> {{Namedfor|Jean-Baptiste Biot‎|name2 = Félix Savart‎}} == Sources == * {{BookReference|Electromagnetism|1990|I.S. Grant|author2 = W.R. Phillips|ed = 2nd|edpage = Second Edition|prev = ?|next = ?}}: Appendix $\text C$: The derivation of the Biot-Savart law Category:Biot-Savart Law")
• 06:22, 21 March 2023 ‎Biot-Savart Law (hist | edit) ‎[1,393 bytes] ‎Prime.mover (talk | contribs) (Created page with "== Theorem == <onlyinclude> Let $s$ be a wire carrying a steady current $I$. Let $\map {\mathbf B} {\mathbf r}$ be the total magnetic field due to $I$ flowing through $s$ at a point $P$ whose position vector is $\mathbf r$. Then: :$\ds \map {\mathbf B} {\mathbf r} = \dfrac {\mu_0 I} {4 \pi} \oint_s \dfrac {\d \mathbf l \time...")
• 03:42, 21 March 2023 ‎Lower Section of Natural Number is Provable (hist | edit) ‎[3,486 bytes] ‎CircuitCraft (talk | contribs) (Created page with "== Theorem == Let $x \in \N$ be a natural number. Then the following WFF: :$\forall y: y = 0 \lor y = \map s 0 \lor \dotso \lor y = \sqbrk x \lor \exists z: \map s z + \sqbrk x = y$ has a formal proof from the axioms of Robinson arithmetic. == Proof == Proceed by induction on $x$. === Base Case === Let $x =...")
• 21:31, 20 March 2023 ‎Interconnection between Vacuum Permittivity and Vacuum Permeability (hist | edit) ‎[2,975 bytes] ‎Prime.mover (talk | contribs) (Created page with "== Motivation behind Vacuum Permittivity and == Vacuum Permeability == <onlyinclude> Right from the start we see the equation $c^2 = \dfrac 1 {\varepsilon_0 \mu_0}$ and we understand immediately that these parameters are tightly wound up in the structure of the electromagnetic spectrum. Hence it is apparent that the Definition:Unit of Measurement|units of meas...")
• 20:36, 20 March 2023 ‎Mean Ergodic Theorem (Hilbert space) (hist | edit) ‎[789 bytes] ‎Usagiop (talk | contribs) (Created page with "== Theorem == <onlyinclude> Let $\GF \in \set {\R, \C}$. Let $\struct {\HH, \innerprod \cdot \cdot_\HH}$ be a Hilbert space over $\mathbb F$. Let $U : \HH \to \HH$ be a bounded linear operator such that: :$\forall f \in \HH : \norm {\map U f}_\HH \le \norm f_\HH$ Let $I := \set {f \in \HH : \map U f = f}$. Let $P : \HH \to I$ denotes the Definition:Orthogonal Projection|orthogon...")
• 17:55, 20 March 2023 ‎Value of Vacuum Permeability/Proof 2 (hist | edit) ‎[1,744 bytes] ‎Prime.mover (talk | contribs) (Created page with "== Theorem == {{:Value of Vacuum Permeability}} == Proof == <onlyinclude> The '''vacuum permeability''' is the physical constant denoted $\mu_0$ defined as: :$\mu_0 := \dfrac 1 {\varepsilon_0c^2}$ where: :$\varepsilon_0$ is the vacuum permittivity defined in $\mathrm F \, \mathrm m^{-1}$ (farads per metre) :$c$ is the Defini...")
• 17:45, 20 March 2023 ‎Value of Vacuum Permeability/Proof 1 (hist | edit) ‎[2,273 bytes] ‎Prime.mover (talk | contribs) (Created page with "== Theorem == {{:Value of Vacuum Permeability}} == Proof == <onlyinclude> The '''vacuum permeability''' is the physical constant denoted $\varepsilon_0$ defined as: :$\mu_0:= \dfrac {2 \alpha h} {e^2 c}$ where: :$e$ is the elementary charge :$\alpha$ is the fine-structure constant :$h$ is Definition:Planck's Constant|Planck's con...")
• 17:30, 20 March 2023 ‎Value of Vacuum Permeability (hist | edit) ‎[876 bytes] ‎Prime.mover (talk | contribs) (Created page with "== Theorem == <onlyinclude> The value of the '''vacuum permeability''' is calculated as: :$\mu_0 = 1 \cdotp 25663 \, 70621 \, 2 (19) \times 10^{-6} \, \mathrm H \, \mathrm m^{-1}$ (henries per metre) with a relative uncertainty of $1 \cdotp 5 \times 10^{-10}$. </onlyinclude> == Proof 1 == {{:Value of Vacuum Pe...")
• 15:34, 20 March 2023 ‎Equality of Terms of Natural Numbers is Provable (hist | edit) ‎[3,845 bytes] ‎CircuitCraft (talk | contribs) (Created page with "== Theorem == Let $A$ and $B$ be terms in the language of arithmetic containing no variables. Let $A = B$ when interpreted over the natural numbers $\N$. Then there is a formal proof of $A = B$ from the axioms of Robinson arithmetic. == Proof == Let $k = A = B$. By Unary Representat...")
• 06:29, 20 March 2023 ‎Coulomb's Law of Electrostatics/SI Units/Also presented as (hist | edit) ‎[1,054 bytes] ‎Prime.mover (talk | contribs) (Created page with "== Coulomb's Law of Electrostatics: Also presented as == :400px|right|thumb|Force Between two Like Charges <onlyinclude> Coulomb's Law of Electrostatics can also be presented as: :$(1): \quad \mathbf F_{a b} = \dfrac 1 {4 \pi \varepsilon_0} \dfrac {q_a q_b \hat {\mathbf r}_{a b} } {r^2}$ ::::where $\hat {\mathbf r}_{a b}$ is the unit vector in the direction from $a$ to $b$. :$(2): \quad \mathbf F_{a b} = \df...")
• 06:20, 20 March 2023 ‎Coulomb's Law of Electrostatics/Also presented as (hist | edit) ‎[735 bytes] ‎Prime.mover (talk | contribs) (Created page with "== Coulomb's Law of Electrostatics: Also presented as == :400px|right|thumb|Force Between two Like Charges <onlyinclude> Coulomb's Law of Electrostatics can also be presented as: :$(1): \quad \mathbf F_{a b} \propto \dfrac {q_a q_b \hat {\mathbf r}_{a b} } {r^2}$ ::::where $\hat {\mathbf r}_{a b}$ is the unit vector in the direction from $a$ to $b$. :$(2): \quad \mathbf F_{a b} \propto \dfrac {q_a q_b} {\siz...")
• 12:50, 19 March 2023 ‎Greatest Common Divisor of Integers/Examples/20, 70 and 80 (hist | edit) ‎[1,660 bytes] ‎Prime.mover (talk | contribs) (Created page with "== Example of Greatest Common Divisor of Integers == <onlyinclude> The greatest common divisor of $20$, $70$ and $80$ is: :$\gcd \set {20, 70, 80} = 10$ </onlyinclude> == Proof == The strictly positive divisors of $20$ are: :$\set {x \in \Z_{>0}: x \divides 20} = \set {1, 2, 4, 5, 10, 20}$ The...")
• 12:39, 19 March 2023 ‎Common Divisor of Integers/Examples/20, 70, 80 (hist | edit) ‎[813 bytes] ‎Prime.mover (talk | contribs) (Created page with "== Example of Common Divisors of Integer == <onlyinclude> The integers $20$, $70$ and $80$ have $2$, $5$ and $10$ as '''common divisors'''. </onlyinclude> * {{BookReference|The Penguin Dictionary of Mathematics|1998|David Nelson|ed = 2nd|edpage = Second Edition|prev = Definition:Common Divisor of Integers|next = Definition:Greatest Common Divisor|entry = common fac...")
• 12:35, 19 March 2023 ‎Common Divisor of Integers/Examples (hist | edit) ‎[288 bytes] ‎Prime.mover (talk | contribs) (Created page with "== Examples of Common Divisors of Integers == <onlyinclude> === $20$, $70$ and $80$ === {{:Common Divisor of Integers/Examples/20, 70, 80}}</onlyinclude> Category:Examples of Common Divisors")
• 10:02, 19 March 2023 ‎Common Denominator/Examples/3, 8, 6 (hist | edit) ‎[883 bytes] ‎Prime.mover (talk | contribs) (Created page with "== Example of Common Denominator == <onlyinclude> The fractions: :$\dfrac 1 3$, $\dfrac 7 8$, $\dfrac 5 6$ all have a common denominator of $24$. Hence: {{begin-eqn}} {{eqn | q = | l = \dfrac 1 3 + \dfrac 7 8 - \dfrac 5 6 | r = \dfrac 8 {24} + \dfrac {21} {24} - \dfrac {20} {24} | c = }} {{eqn | r = \dfrac {8 + 21 - 20} {24} | c = }} {{eqn | r...")
• 09:26, 19 March 2023 ‎Common Denominator/Examples/Multiples of 12 (hist | edit) ‎[646 bytes] ‎Prime.mover (talk | contribs) (Created page with "== Examples of Common Denominators == <onlyinclude> Multiples of $1$ are all common denominators of: :$\dfrac 1 2$, $\dfrac 1 4$, $\dfrac 1 6$ Hence these fractions can be expressed as: :$\dfrac 6 {12}$, $\dfrac 3 {12}$, $\dfrac 2 {12}$ </onlyinclude> == Sources == * {{BookReference|Dictionary of Mathematics|1989|Ephraim J. Borowski|author2...")
• 09:04, 19 March 2023 ‎Common Denominator/Examples/2, 3, 7 (hist | edit) ‎[914 bytes] ‎Prime.mover (talk | contribs) (Created page with "== Examples of Common Denominators == <onlyinclude> The fractions: :$\dfrac 1 2$, $\dfrac 1 3$, $\dfrac 3 7$ have common denominators: :$42$, $84$, $126$, $168$ and so on. </onlyinclude> == Sources == * {{BookReference|The Penguin Dictionary of Mathematics|1998|David Nelson|ed = 2nd|edpage = Second Edition|prev = Definition:Common Denominator|next = Definition:Lowest Co...")
• 08:57, 19 March 2023 ‎Common Denominator/Examples (hist | edit) ‎[482 bytes] ‎Prime.mover (talk | contribs) (Created page with "== Examples of Common Denominators == <onlyinclude> === Multiples of $12$ === {{:Common Denominator/Examples/Multiples of 12}} === $2$, $3$ and $7$ === {{:Common Denominator/Examples/2, 3, 7}} === $3$, $8$ and $6$ === {{:Common Denominator/Examples/3, 8, 6}}</onlyinclude> Category:Examples of Common Denomin...")
• 08:51, 19 March 2023 ‎Incommensurable/Examples/Root 2 and 1 (hist | edit) ‎[868 bytes] ‎Prime.mover (talk | contribs) (Created page with "== Example of Incommensurability == <onlyinclude> $\sqrt 2$ and $1$ are '''incommensurable'''. </onlyinclude> == Proof == From Square Root of 2 is Irrational, the ratio $\sqrt 2$ to $1$ is irrational. Hence the result by definition of incommensurable. {{qed}} == Sources == * {{BookReference|The Penguin Dictionary of Mathema...")
• 08:47, 19 March 2023 ‎Incommensurable/Examples (hist | edit) ‎[251 bytes] ‎Prime.mover (talk | contribs) (Created page with "== Examples of Incommensurability == <onlyinclude> === $\sqrt 2$ and $1$ === {{:Incommensurable/Examples/Root 2 and 1}}</onlyinclude> Category:Examples of Incommensurability")
• 08:45, 19 March 2023 ‎Commensurable/Examples/3 Feet and 2 Inches (hist | edit) ‎[1,075 bytes] ‎Prime.mover (talk | contribs) (Created page with "== Example of Commensurability == <onlyinclude> The lengths $2$ inches and $3$ feet are '''commensurable'''. </onlyinclude> == Proof == $3$ feet is $18$ times $2$ inches. Hence $2$ inches is a common divisor of both $2$ Definition:...")

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