Talk:Modular equivalence

From Why start at x, y, z
Revision as of 13:31, 11 July 2021 by Christian Lawson-Perfect (talk | contribs) (Christian Lawson-Perfect moved page Talk:Mod Notation to Talk:Modular equivalence)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

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:

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:

Alternate mod notation as rendered in Latex

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

--Christian Lawson-Perfect (talk) 15:06, 10 July 2021 (UTC)