# New pages

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- 03:00, 22 May 2018 Translation of Index Variable of Summation/Infinite Series (hist) [1,095 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $R: \Z \to \left\{ {\mathrm T, \mathrm F}\right\}$ be a propositional function on the set of Definition:Integer|inte...")
- 02:55, 22 May 2018 Sum of Summations over Overlapping Domains/Infinite Series (hist) [1,428 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $R: \Z \to \left\{ {\mathrm T, \mathrm F}\right\}$ and $S: \Z \to \left\{ {\mathrm T, \mathrm F}\right\}$ be Definition:Propositional Function|proposition...")
- 18:03, 21 May 2018 Summation of i from 1 to n of Summation of j from 1 to i/Example (hist) [1,334 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Summation of $i$ from $1$ to $n$ of Summation of $j$ from $1$ to $i$ == {{:Summation of i from 1 to...")
- 09:10, 21 May 2018 Argument of x to the n Equals n Times The Argument (hist) [555 bytes] Antimatterexplosion (talk | contribs) (I feel this should be cited on Machin's Formula for Pi/Proof 2)
- 01:48, 21 May 2018 Summation/Inequality/Examples/From 1 to Pi (hist) [864 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Summation by Inequality == <onlyinclude> Let $n = 3 \cdotp 1 4$. Then: :$\sum_{1 \mathop \le j \mathop \le n} a_j = a_1 +...")
- 19:17, 19 May 2018 Reciprocal of Logarithm/Examples/Logarithm Base 10 of 2 (hist) [680 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Reciprocal of Logarithm == <onlyinclude> The reciprocal of $\log_{10} 2$ is $\log_2 10$. </onlyinclude> == Proof == From Recipr...")
- 19:16, 19 May 2018 Reciprocal of Logarithm/Examples (hist) [267 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Reciprocal of Logarithm == <onlyinclude> === Logarithm Base $10$ of $2$ === {{:Reciprocal of Log...")
- 18:47, 19 May 2018 Number of Bits for Decimal Integer/Examples/14 Digits (hist) [1,260 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Number of Bits for Decimal Integer == <onlyinclude> A positive integer $n \in \Z_{>0}$ which has $14$ Definition:D...")
- 18:40, 19 May 2018 Number of Bits for Decimal Integer/Examples (hist) [270 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Number of Bits for Decimal Integer == <onlyinclude> === $14$ Digits === {{:Number of Bits for Deci...")
- 16:27, 19 May 2018 Number of Bits for Decimal Integer (hist) [1,183 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $n \in \Z_{>0}$ be a (strictly) positive integer. Let $n$ have $m$ digits when expressed in [...")
- 11:57, 19 May 2018 Number of Digits to Represent Integer in Given Number Base (hist) [1,205 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $n \in \Z_{>0}$ be a (strictly) positive integer. Let $b \in \Z$ be an integer such that $b...")
- 08:30, 19 May 2018 Change of Base of Logarithm/Base 2 to Base 8 (hist) [1,126 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\log_8 x$ be the logarithm base $8$ of $x$. Let $\lg x$ be the [[Definition:Binary Logarithm|binary (base $2$) logarithm]...")
- 08:18, 19 May 2018 General Logarithm/Examples/Base b of -1 (hist) [937 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $b \in \R_{>0}$ be a strictly positive real number such that $b \ne 1$. Let $\log_b$ denote the Definition:R...")
- 08:10, 19 May 2018 General Logarithm/Examples/Base b of 1 (hist) [1,012 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $b \in \R_{>0}$ be a strictly positive real number such that $b \ne 1$. Let $\log_b$ denote the Definition:R...") originally created as "General Logarithm of 1 is 0"
- 07:36, 19 May 2018 Logarithm to Own Base equals 1 (hist) [656 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $b \in \R_{>0}$ be a strictly positive real number such that $b \ne 1$. Let $\log_a$ denote the Definition:R...")
- 07:32, 19 May 2018 General Logarithm/Examples/Base Pi of Pi (hist) [656 bytes] Prime.mover (talk | contribs) (Created page with "== Example of General Logarithm == <onlyinclude> The logarithm base $\pi$ of...")
- 07:15, 19 May 2018 Root of Quotient equals Quotient of Roots (hist) [1,525 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $a, b \in \R_{>0}$ be (strictly) positive real numbers. Let $n \in \Z_{>0}$ be a Definition:Strictly Positiv...")
- 04:40, 19 May 2018 Change of Base of Logarithm/Base 10 to Base 2 (hist) [805 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\log_{10} x$ be the common (base $10$) logarithm of $x$. Let $\lg x$ be the Definition:Binary Logarithm|binary (base $2$...")
- 03:39, 19 May 2018 Change of Base of Logarithm/Base e to Base 10/Form 2 (hist) [1,051 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\log_{10} x$ be the common (base $10$) logarithm of $x$. Let $\log_e x$ be the Definition:Natural Logarithm|natural (bas...")
- 03:35, 19 May 2018 Change of Base of Logarithm/Base e to Base 10/Form 1 (hist) [941 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\log_{10} x$ be the common (base $10$) logarithm of $x$. Let $\log_e x$ be the Definition:Natural Logarithm|natural (bas...")
- 03:33, 19 May 2018 Change of Base of Logarithm/Base 10 to Base e/Form 2 (hist) [700 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\log_e x$ be the natural (base $e$) logarithm of $x$. Let $\log_{10} x$ be the Definition:Common Logarithm|common (base...")
- 03:25, 19 May 2018 Change of Base of Logarithm/Base 10 to Base e/Form 1 (hist) [946 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\log_e x$ be the natural (base $e$) logarithm of $x$. Let $\log_{10} x$ be the Definition:Common Logarithm|common (base...")
- 19:46, 18 May 2018 General Logarithm/Examples (hist) [532 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of General Logarithm == <onlyinclude> === General Logarithm: $\log_\pi \pi$ === {{:Ge...")
- 19:40, 18 May 2018 Binary Logarithm/Examples/32 (hist) [755 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Binary Logarithm == <onlyinclude> The binary logarithm of $32$ is: :$\lg 32 = 5$ </onlyinclude>...")
- 14:05, 18 May 2018 Necessary Precision for x equal to log base 10 of 2 to determine Decimal expansion of 10 to the x (hist) [1,129 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $b = 10$. Let $x \approx \log_{10} 2$. Let it be necessary to calculate the decimal expansion of $x$ to determine the fir...")
- 03:15, 18 May 2018 Logarithm Base 10 of 2 is Irrational/Proof 2 (hist) [365 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == {{:Logarithm Base 10 of 2 is Irrational}} == Proof == <onlyinclude> Because $5$ is a divisor of $10$, it cannot be the case th...")
- 03:12, 18 May 2018 Logarithm Base 10 of 2 is Irrational/Proof 1 (hist) [957 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == {{:Logarithm Base 10 of 2 is Irrational}} == Proof == <onlyinclude> {{AimForCont}} $\log_{10} 2$ is rational. Then: {{begin-eqn}...")
- 03:00, 18 May 2018 Ordering on Real Numbers from Decimal Expansion (hist) [1,130 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $x, y \in \R$ be real numbers. Let $x$ and $y$ be expressed by their decimal expansions: {{be...")
- 02:27, 18 May 2018 Witch of Agnesi/Historical Note (hist) [325 bytes] Prime.mover (talk | contribs) (Created page with "== Historical Note on Witch of Agnesi == <onlyinclude> While the Witch of Agnesi is named for {{AuthorRef|Maria Gaëtana Agnesi}}, its study does not actually originat...")
- 02:24, 18 May 2018 Witch of Agnesi/Linguistic Note (hist) [787 bytes] Prime.mover (talk | contribs) (Created page with "== Linguistic Note on Witch of Agnesi == <onlyinclude> The word '''witch''' appears to be a mistranslation from the Italian '''vertere''' ('''to turn''': the term comes fr...")
- 01:21, 18 May 2018 Power (Algebra)/Rational Number/Examples/0.125 to the Power of Minus Two Thirds (hist) [812 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Rational Power == <onlyinclude> :$0 \cdotp 125^{-2/3} = 4$ </onlyinclude> == Proof == {{begin-eqn}} {{eqn | l = 0 \cdotp 125^{-2/...")
- 18:28, 17 May 2018 Power (Algebra)/Integer/Examples/Minus 3 to the Power of Minus 3 (hist) [789 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Integer Power == <onlyinclude> :$-3^{-3} = -\dfrac 1 {27}$ </onlyinclude> == Proof == {{begin-eqn}} {{eqn | l = -3^{-3} | r...")
- 17:30, 17 May 2018 Smallest Strictly Positive Rational Number does not Exist (hist) [1,390 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == There exists no smallest element of the set of Definition:Strictly Positive Rational Number|strictly positi...")
- 16:49, 17 May 2018 Change of Base of Logarithm/Base 2 to Base 10 (hist) [1,136 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $\log_{10} x$ be the common (base $10$) logarithm of $x$. Let $\lg x$ be the Definition:Binary Logarithm|binary (base $2$...")
- 16:38, 17 May 2018 Change of Base of Logarithm/Examples (hist) [775 bytes] Prime.mover (talk | contribs) (Created page with "== Examples of Change of Base of Logarithm == <onlyinclude> === Base $10$ to Base $e$ === {{:Change of Base of Logarithm/...")
- 16:04, 17 May 2018 Power to Real Number by Decimal Expansion is Uniquely Defined (hist) [1,749 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $r \in \R_{> 1}$ be a real number greater than $1$, expressed by its decimal expansion: :$r = n...")
- 17:46, 16 May 2018 Alternating Sum of Sequence of Odd Cubes over Fourth Power plus 4 (hist) [6,737 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == {{begin-eqn}} {{eqn | l = \sum_{k \mathop = 1}^n \dfrac {\left({-1}\right)^k \left({2 k + 1}\right)^3} {\left({2 k + 1}\right)^4 + 4} | r = \frac {1^3} {1...")
- 16:59, 16 May 2018 Upper Bound for Harmonic Number (hist) [1,389 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == :$H_{2^m} \le 1 + m$ where $H_{2^m}$ denotes the $2^m$th harmonic number. == Proof == :$\displaystyle \sum_{n \mathop = 1}^\i...")
- 16:22, 16 May 2018 Harmonic Numbers/Examples/H2 (hist) [749 bytes] Prime.mover (talk | contribs) (Created page with "== Example of Harmonic Number == <onlyinclude> :$H_2 = \dfrac 3 2$ </onlyinclude> where $H_2$ denotes the second Definition:Harmonic Number|ha...")
- 01:25, 16 May 2018 Sum of Sequence of Harmonic Numbers/Proof 2 (hist) [1,472 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == {{:Sum of Sequence of Harmonic Numbers}} == Proof == <onlyinclude> From Sum over k to n of k Choose m by kth Harmonic Number: :$\sum_{k \mathop = 1}^n \bino...")
- 01:14, 16 May 2018 Sum of Sequence of Harmonic Numbers/Proof 1 (hist) [1,012 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == {{:Sum of Sequence of Harmonic Numbers}} == Proof == <onlyinclude> {{begin-eqn}} {{eqn | l = \sum_{k \mathop = 1}^n H_k | r = \sum_{k \mathop = 1}^n \left...")
- 18:21, 15 May 2018 Sum over k to n of k Choose m by kth Harmonic Number (hist) [1,807 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == :$\displaystyle \sum_{k \mathop = 1}^n \binom k m H_k = \binom {n + 1} {m + 1} \left({H_{n + 1} - \frac 1 {m + 1} }\right)$ where: : $\dbinom k m$ denotes a ...")
- 17:40, 15 May 2018 Sum of Sequence of Harmonic Numbers (hist) [515 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == :$\displaystyle \sum_{k \mathop = 1}^n H_k = \left({n + 1}\right) H_n - n$ where $H_k$ denotes the $k$th harmonic number. == P...")
- 16:57, 15 May 2018 Riemann Zeta Function of 8/Historical Note (hist) [344 bytes] Prime.mover (talk | contribs) (Created page with "== Historical Note on Riemann Zeta Function of 8 == <onlyinclude> The Riemann Zeta Function of 8 was solved by {{AuthorRef|Leonhard Paul Euler|Leonhard Euler}}, using...")
- 16:56, 15 May 2018 Riemann Zeta Function of 8 (hist) [1,345 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == <onlyinclude> :$\displaystyle \zeta \left({8}\right) = \sum_{n \mathop = 1}^{\infty} \frac 1 {n^8} = \frac {\pi^8} {9450}$ where $\zeta$ denotes the Definition...")
- 06:03, 15 May 2018 Logarithmic Approximation of Error Term of Stirling's Formula for Gamma Function (hist) [900 bytes] Caliburn (talk | contribs) (extracting out)
- 02:26, 15 May 2018 Approximate Size of Sum of Harmonic Series (hist) [845 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $H_n$ denote the sum of the harmonic series. Then $H_n$ can be approximated as follows: :$H_n \appr...")
- 18:06, 14 May 2018 Falling Factorial of Sum of Integers (hist) [1,049 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $r \in \R$ be a real number. Let $a, b \in \Z$ be (positive) integers. Then: :$r^{\underline {a...")
- 15:31, 14 May 2018 Binomial Coefficient of Minus Half (hist) [1,021 bytes] Prime.mover (talk | contribs) (Created page with "== Theorem == Let $k \in \Z$. :$\dbinom {-\frac 1 2} k = \dfrac 1 {4^k} \dbinom {2 k} k$ where $\dbinom r k$ denotes a Definition:Binomial Coefficient|binomial coefficien...")
- 14:03, 14 May 2018 Provable Consequence of Theorems is Theorem (hist) [2,642 bytes] Lord Farin (talk | contribs) (Created page with "== Theorem == Let $\mathcal P$ be a proof system for a formal language $\mathcal L$. Let $\mathcal F$ be a collect...")