String homomorphisms are monoid morphisms on the free monoid, preserving the empty string and the binary operation of string concatenation.
32.
For the sake of simplicity, unless otherwise specified, a " left " external binary operation is implied.
33.
I was treating infinity as an ideal element and exponentiation as a notational convenience, referring to an abstract binary operation.
34.
If the cross product is defined as a binary operation, it takes as " input " exactly two vectors.
35.
The relation d " introduced in this way defines a partial ordering from which the binary operation'" may be recovered.
36.
Both are names sometimes given to a set with a binary operation with no other assumptions ( especially, not associativity ).
37.
A binary operation \ scriptstyle * : A \ times A \ to \ mathfrak { G } is anticommutative if and only if
38.
In mathematics, a "'set, together with a binary operation satisfying certain axioms, detailed in the group article.
39.
Comprehensions, also called aggregates operations or reductions, are OptimJ expressions that extend a given binary operation over a collection of values.
40.
All strictly increasing associative binary operations on the real numbers are isomorphic to multiplication of numbers in the interval [ 0, 1 ].
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