Difference between revisions of "Category:Unpleasantness"

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(Mod Notation)
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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'.  
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'.  
The following 3 Latex macros are used to produce the alternate notation suggested below:
[[File:modmacros.png|Alternate mod notation macros]]


Examples:  
Examples:  

Revision as of 17:06, 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'.

The following 3 Latex macros are used to produce the alternate notation suggested below:

Alternate mod notation 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 $77\bmq{13}{5}12$.

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.