This one is experimental. I'm trying to get at a notation that allows me to investigate equations where there are multiple modular operations form different bases.(adsbygoogle = window.adsbygoogle || []).push({});

Define

Anatural variablex or a can take on any natural value and zero if the context allows.

And then

1) [itex]\underline{x}[/itex] deal with x as a constant

2) [itex]x_{[\underline{a}]}=x mod \underline{a}[/itex] equals the set of residues modulo a

3) [itex]x_{[a]}=x mod a[/itex] equals the set of natural numbers since a is assumed to be a variable in this notation

4) [itex]\underline x_{[\underline{a}]}=\underline{x} mod \underline{a}[/itex] is a generic way of writing one specific residue of a, the following are equivalent 3 mod 4, 7 mod 4, etc.

5) [tex]\underline x_{[a]}=\underline{x} mod a[/itex] is equivalent to the set [itex]\{0,1,...,\underline{x}\}[/itex].

operations and multiple base maps.

Consider [itex]x_{[\underline{a},\underline{b}]} =_{[\underline{c}]} y_{[\underline{d}]}[/itex]

It says first evaluate x mod a then mod b, and evaluate y mod d, then solve the resulting equation mod c.

Multiplication now requires a symbol, juxtiposition no longer works. [itex]x \times_{[\underline{a}]} y = \underline{c}[/itex] means x and y are natural variables so find natural numbers that can be multiplied mod a to yield c. Since the base quantifier is missing on the equals sign there may not be a solution. Whereas [itex]x \times_{[\underline{a}]} y =_{[\underline{a}]} \underline{c}[/itex] means solkve the equation mod a as well.

The same works for addition [itex]x +_{[\underline{a}]} y = \underline{c}[/itex]

The obvious question is why make such a notation? Are there any problems where solving muddled equations is necessary? Does the notation help facilitate either the understanding of the problems or their solution?

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Muddled Equations

Loading...

Similar Threads - Muddled Equations | Date |
---|---|

I Solutions to equations involving linear transformations | Mar 6, 2018 |

I Solving System of Equations w/ Gauss-Jordan Elimination | Sep 18, 2017 |

**Physics Forums - The Fusion of Science and Community**