https://whystartat.xyz/api.php?action=feedcontributions&user=RJBoland&feedformat=atomWhy start at x, y, z - User contributions [en-gb]2022-12-03T22:31:43ZUser contributionsMediaWiki 1.36.1https://whystartat.xyz/index.php?title=Talk:Modular_equivalence&diff=138Talk:Modular equivalence2021-07-02T18:28:24Z<p>RJBoland: Alternate Mod Notation</p>
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<div>[[Category:Unpleasantness]]<br />
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Mod notation can be bulky and counter-intuitive. Here is an alternate mod notation that simply removes the middle line from the equivalence sign, places the modulus inside and drops the now moot 'mod'. <br />
<br />
The following macros are defined for the Latex that follows and the second graphic shows the result:<br />
<br />
[[File:Modmacros.png|left|alt=Alternate mod Latex macros|Alternate mod Latex macros]]<br />
<br />
Examples: <br />
In lieu of $x\equiv y \mod{z}$, we have $x\bm{z}y$<br />
<br />
Rather than take both sides $\mod{m}$, we would take both sides $\bm{m}$<br />
<br />
Taking all $m\bm{7}1\in \mathbb{Z}_{+}$ gives $\{1,8,15,\dots\}$<br />
<br />
A non-equivalence can be written $9\bmn{4}3$<br />
<br />
It can be chained ala $27\bm{11}5\bm{3}2$<br />
<br />
and even be adapted to carry quotient information as in $77\bmq{13}{5}12$. <br />
<br />
Here's how that looks when rendered:<br />
<br />
[[File:Modexamples.png|left|alt=Alternate mod notation as rendered in Latex|Alternate mod notation as rendered in Latex]]</div>RJBolandhttps://whystartat.xyz/index.php?title=Talk:Modular_equivalence&diff=137Talk:Modular equivalence2021-07-02T18:24:36Z<p>RJBoland: </p>
<hr />
<div>[[Category:Unpleasantness]]<br />
<br />
Mod notation can be bulky and counter-intuitive. Here is an alternate mod notation that simply removes the middle line from the equivalence sign, places the modulus inside and drops the now moot 'mod'. <br />
<br />
The following macros are defined for the Latex that follows and the second graphic shows the result:<br />
<br />
[[File:Modmacros.png|left|alt=Alternate mod Latex macros|Alternate mod Latex macros]]<br />
<br />
Examples: <br />
In lieu of $x\equiv y \mod{z}$, we have $x\bm{z}y$<br />
Rather than take both sides $\mod{m}$, we would take both sides $\bm{m}$<br />
Taking all $m\bm{7}1\in \mathbb{Z}_{+}$ gives $\{1,8,15,\dots\}$<br />
A non-equivalence can be written $9\bmn{4}3$<br />
It can be chained ala $27\bm{11}5\bm{3}2$<br />
and even be adapted to carry quotient information as in $77\bmq{13}{5}12$. <br />
<br />
Here's how that looks when rendered:<br />
<br />
[[File:Modexamples.png|left|alt=Alternate mod notation as rendered in Latex|Alternate mod notation as rendered in Latex]]</div>RJBolandhttps://whystartat.xyz/index.php?title=Talk:Modular_equivalence&diff=136Talk:Modular equivalence2021-07-02T18:23:57Z<p>RJBoland: Alternate Mod Notation</p>
<hr />
<div>[[Category:Unpleasantness]]<br />
<br />
Mod notation can be bulky and counter-intuitive. Here is an alternate mod notation that simply removes the middle line from the equivalence sign, places the modulus inside and drops the now moot 'mod'. <br />
<br />
The following macros are defined for the Latex that follows and the second graphic shows the result:<br />
<br />
[[File:Modmacros.png|left|alt=Alternate mod Latex macros|Alternate mod Latex macros]]<br />
<br />
Examples: <br />
In lieu of $x\equiv y \mod{z}$, we have $x\bm{z}y$<br />
Rather than take both sides $\mod{m}$, we would take both sides $\bm{m}$<br />
Taking all $m\bm{7}1\in \mathbb{Z}_{+}$ gives $\{1,8,15,\dots\}$<br />
A non-equivalence can be written $9\bmn{4}3$<br />
It can be chained ala $27\bm{11}5\bm{3}2$<br />
and even be adapted to carry quotient information as in $77\bmq{13}{5}12$. <br />
<br />
Here's how that looks when rendered:<br />
<br />
[[File:Modexamples.png|left|alt=Alternate mod notation as rendered in Latex|Alternate mod notation as rendered in Latex]]<br />
<br />
This notation is more compact, intuitive, flexible, prettier, puts the modulus in the middle where it belongs and there is no dead mathematician named Mod being dishonored and forgotten and even if there were, he or she should be.</div>RJBolandhttps://whystartat.xyz/index.php?title=File:Modexamples.png&diff=135File:Modexamples.png2021-07-02T18:21:28Z<p>RJBoland: </p>
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<div>Alternate mod examples rendered in Latex</div>RJBolandhttps://whystartat.xyz/index.php?title=Talk:Modular_equivalence&diff=134Talk:Modular equivalence2021-07-02T18:14:38Z<p>RJBoland: Alternate Mod Notation</p>
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<div>[[Category:Unpleasantness]]<br />
<br />
Alternate Mod Notation</div>RJBolandhttps://whystartat.xyz/index.php?title=Modular_equivalence&diff=133Modular equivalence2021-07-02T17:22:16Z<p>RJBoland: Blanked the page</p>
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<div></div>RJBolandhttps://whystartat.xyz/index.php?title=Category:Unpleasantness&diff=132Category:Unpleasantness2021-07-02T17:20:58Z<p>RJBoland: Blanked the page</p>
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<div></div>RJBolandhttps://whystartat.xyz/index.php?title=Category:Unpleasantness&diff=131Category:Unpleasantness2021-07-02T17:19:20Z<p>RJBoland: Mod Notation</p>
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<div>[[Category:Unpleasantness]]</div>RJBolandhttps://whystartat.xyz/index.php?title=Category:Unpleasantness&diff=130Category:Unpleasantness2021-07-02T17:15:45Z<p>RJBoland: Blanked the page</p>
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<div></div>RJBolandhttps://whystartat.xyz/index.php?title=Modular_equivalence&diff=129Modular equivalence2021-07-02T17:15:08Z<p>RJBoland: Mod Notation</p>
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<div>Mod Notation Test</div>RJBolandhttps://whystartat.xyz/index.php?title=Category:Unpleasantness&diff=128Category:Unpleasantness2021-07-02T17:14:15Z<p>RJBoland: Mod Notation</p>
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<div>[[Mod Notation]]<br />
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test</div>RJBolandhttps://whystartat.xyz/index.php?title=Category:Unpleasantness&diff=127Category:Unpleasantness2021-07-02T17:06:28Z<p>RJBoland: </p>
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<div>Mod notation can be bulky and counter-intuitive. Here is a mod notation that simply removes the middle line from the equivalence sign, places the modulus inside and drops the now moot 'mod'. <br />
<br />
The following 3 Latex macros are used to produce the alternate notation suggested below:<br />
<br />
[[File:modmacros.png|Alternate mod notation macros]]<br />
<br />
<br />
Examples: <br />
<br />
In lieu of $x\equiv y \mod{z}$, we have $x\bm{z}y$<br />
<br />
<br />
Rather than take both sides $\mod{m}$, we would take both sides $\bm{m}$<br />
<br />
<br />
Taking all $m\bm{7}1\in \mathbb{Z}_{+}$ gives $\{1,8,15,\dots\}$<br />
<br />
<br />
A non-equivalence can be written $9\bmn{4}3$<br />
<br />
<br />
It can be chained ala $27\bm{11}5\bm{3}2$<br />
<br />
<br />
and even be adapted to carry quotient information as in $77\bmq{13}{5}12$. <br />
<br />
It is better because it is more compact, intuitive, flexible, prettier, puts the modulus in the middle where it belongs and there is no dead mathematician named Mod being dishonored and forgotten and even if there were, he or she should be.</div>RJBolandhttps://whystartat.xyz/index.php?title=Category:Unpleasantness&diff=126Category:Unpleasantness2021-07-02T17:00:32Z<p>RJBoland: Mod Notation</p>
<hr />
<div>Mod notation can be bulky and counter-intuitive. Here is a mod notation that simply removes the middle line from the equivalence sign, places the modulus inside and drops the now moot 'mod'. <br />
<br />
Examples: <br />
<br />
In lieu of $x\equiv y \mod{z}$, we have $x\bm{z}y$<br />
<br />
<br />
Rather than take both sides $\mod{m}$, we would take both sides $\bm{m}$<br />
<br />
<br />
Taking all $m\bm{7}1\in \mathbb{Z}_{+}$ gives $\{1,8,15,\dots\}$<br />
<br />
<br />
A non-equivalence can be written $9\bmn{4}3$<br />
<br />
<br />
It can be chained ala $27\bm{11}5\bm{3}2$<br />
<br />
<br />
and even be adapted to carry quotient information as in $77\bmq{13}{5}12$. <br />
<br />
It is better because it is more compact, intuitive, flexible, prettier, puts the modulus in the middle where it belongs and there is no dead mathematician named Mod being dishonored and forgotten and even if there were, he or she should be.</div>RJBolandhttps://whystartat.xyz/index.php?title=File:Modmacros.png&diff=125File:Modmacros.png2021-07-02T16:27:16Z<p>RJBoland: </p>
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<div>Latex Macros for better mod notation</div>RJBoland