definition
The quality of agreeing or corresponding; being suitable and appropriate.
definition
A relation between two numbers indicating they give the same remainder when divided by some given number.
definition
The quality of being isometric — roughly, the same measure and shape.
definition
More generally: any equivalence relation defined on an algebraic structure which is preserved by operations defined by the structure.
Under the general heading "Algebra and Theory of Numbers" occur the subheadings "Elements of Algebra," with the topics rational polynomials, permutations, &c., partitions, probabilities; "Linear Substitutions," with the topics determinants, &c., linear substitutions, general theory of quantics; "Theory of Algebraic Equations," with the topics existence of roots, separation of and approximation to, theory of Galois, &c. "Theory of Numbers," with the topics congruences, quadratic residues, prime numbers, particular irrational and transcendental numbers.
A loop is simple if it has no nontrivial congruences.
Proving the correctness of these structural congruences is the task I hope to finish in the near future.
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