Difference between revisions of "Meta-Rule/Composition"
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=Symmetries as the first Meta-Rule= | =Symmetries as the first Meta-Rule= | ||
According to [[Mathemaniac]], symmetries can be thought of as mathematical operands that gets to be manipulated through some operations that preserves the properties of being symmetrical. These four most general properties are: | According to [[Mathemaniac]], symmetries can be thought of as mathematical operands that gets to be manipulated through some operations that preserves the properties of being symmetrical. These four most general properties are: | ||
# Closure: Symmetrical operations on symmetries always create symmetries | # [[Closure]]: Symmetrical operations on symmetries always create [[Symmetry|symmetries]] | ||
# Associativity: Symmetries composition with symmetries are symmetries Associative | # [[Associativity]]: Symmetries composition with symmetries are symmetries Associative | ||
# Identity: Doing nothing is a symmetrical operation | # [[Identity]]/[[Unit]]: Doing nothing is a symmetrical operation | ||
# Inverse Exists: Symmetrical operations can be undone, and returns to the original symmetry. | # [[Inverse]] Exists: Symmetrical operations can be undone, and returns to the original symmetry. | ||
<noinclude> | <noinclude> | ||
[[Definition::Meta-Rule]] | [[Definition::Meta-Rule]] | ||
</noinclude> | </noinclude> | ||
Revision as of 11:52, 27 July 2021
Symmetries as the first Meta-Rule
According to Mathemaniac, symmetries can be thought of as mathematical operands that gets to be manipulated through some operations that preserves the properties of being symmetrical. These four most general properties are:
- Closure: Symmetrical operations on symmetries always create symmetries
- Associativity: Symmetries composition with symmetries are symmetries Associative
- Identity/Unit: Doing nothing is a symmetrical operation
- Inverse Exists: Symmetrical operations can be undone, and returns to the original symmetry.