Category:Unpleasantness: Difference between revisions
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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'. | |||
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 $77\bmq{13}{5}12$. | |||
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. | |||
Revision as of 17:00, 2 July 2021
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'.
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 $77\bmq{13}{5}12$.
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.
Pages in category ‘Unpleasantness’
The following 10 pages are in this category, out of 10 total.
