Talk:Modular equivalence - Revision history

Christian Lawson-Perfect: Christian Lawson-Perfect moved page Talk:Mod Notation to Talk:Modular equivalence

2021-07-11T13:31:47Z

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Revision as of 14:31, 11 July 2021

2021-07-10T15:06:35Z

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	[[File:Modexamples.png\|left\|alt=Alternate mod notation as rendered in Latex\|Alternate mod notation as rendered in Latex]]		[[File:Modexamples.png\|left\|alt=Alternate mod notation as rendered in Latex\|Alternate mod notation as rendered in Latex]]

			<hr/>

			Would $7 \underset{3}{=} 1$ work similarly?

			--[[User:Christian Lawson-Perfect\|Christian Lawson-Perfect]] ([[User talk:Christian Lawson-Perfect\|talk]]) 15:06, 10 July 2021 (UTC)

2021-07-02T18:28:24Z

Alternate Mod Notation

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	Examples:		Examples:
	In lieu of $x\equiv y \mod{z}$, we have $x\bm{z}y$		In lieu of $x\equiv y \mod{z}$, we have $x\bm{z}y$

	Rather than take both sides $\mod{m}$, we would take both sides $\bm{m}$		Rather than take both sides $\mod{m}$, we would take both sides $\bm{m}$

	Taking all $m\bm{7}1\in \mathbb{Z}_{+}$ gives $\{1,8,15,\dots\}$		Taking all $m\bm{7}1\in \mathbb{Z}_{+}$ gives $\{1,8,15,\dots\}$

	A non-equivalence can be written $9\bmn{4}3$		A non-equivalence can be written $9\bmn{4}3$

	It can be chained ala $27\bm{11}5\bm{3}2$		It can be chained ala $27\bm{11}5\bm{3}2$

	and even be adapted to carry quotient information as in $77\bmq{13}{5}12$.		and even be adapted to carry quotient information as in $77\bmq{13}{5}12$.

2021-07-02T18:24:36Z

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	[[File:Modexamples.png\|left\|alt=Alternate mod notation as rendered in Latex\|Alternate mod notation as rendered in Latex]]		[[File:Modexamples.png\|left\|alt=Alternate mod notation as rendered in Latex\|Alternate mod notation as rendered in Latex]]

	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.

2021-07-02T18:23:57Z

Alternate Mod Notation

← Older revision		Revision as of 19:23, 2 July 2021
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	[[Category:Unpleasantness]]		[[Category:Unpleasantness]]

	Alternate Mod ~~Notation~~		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'.

			The following macros are defined for the Latex that follows and the second graphic shows the result:

			[[File:Modmacros.png\|left\|alt=Alternate mod Latex macros\|Alternate mod Latex macros]]

			Examples:
			In lieu of $x\equiv y \mod{z}$, we have $x\bm{z}y$
			Rather than take both sides $\mod{m}$, we would take both sides $\bm{m}$
			Taking all $m\bm{7}1\in \mathbb{Z}_{+}$ gives $\{1,8,15,\dots\}$
			A non-equivalence can be written $9\bmn{4}3$
			It can be chained ala $27\bm{11}5\bm{3}2$
			and even be adapted to carry quotient information as in $77\bmq{13}{5}12$.

			Here's how that looks when rendered:

			[[File:Modexamples.png\|left\|alt=Alternate mod notation as rendered in Latex\|Alternate mod notation as rendered in Latex]]

			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.

2021-07-02T18:14:38Z

Alternate Mod Notation

New page

[[Category:Unpleasantness]]

Alternate Mod Notation