Examples of using Binary operations in English and their translations into Indonesian
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Rings and fields- structures with two binary operations.
Has two binary operations(+) and(×), with× distributive over+.
An algebraic structure or an algebraic system is a non-empty set together with one ormore binary operations on that set.
A ring has two binary operations(+) and(×), with× distributive over.
For all a, b in F, both a+ b anda· b are in F(or more formally,+ and· are binary operations on F).
This property is shared by most binary operations, but not subtraction or division.
For all a, b belonging to F, both a+ b anda* b belong to F(or more formally,+ and* are binary operations on F);
OptionBit is a good binary operations broker that enjoys an excellent reputation among its traders.
However, both in universal algebra and model theory the binary operations considered are defined on all of S× S.
Typical examples of binary operations are the addition(+) and multiplication(×) of numbers and matrices as well as composition of functions on a single set.
Thus, for the general, non-associative case, binary operations can be represented with binary trees.
Typical examples of binary operations are the addition(+) and multiplication(×) of numbers and matrices as well as composition of functions on a single set.
Note however that both in algebra and model theory the binary operations considered are defined on the whole of.
Binary operations are the keystone of most algebraic structures, that are studied in algebra, and used in all mathematics, such as fields, groups, monoids, rings, algebras, and many more.
While for nonempty set with two binary operations which fulfill the certain natures is called ring.
Binary operations are often written using infix notation such as a∗ b, a+ b, a· b or(by juxtaposition with no symbol) ab rather than by functional notation of the form fa, b.
Note however that both in algebra and model theory the binary operations considered are defined on all of$\small S\times S$.
Many binary operations of interest in both algebra and formal logic are commutative, satisfying f(a, b) f(b, a) for all elements a and b in S, or associative, satisfying f(f(a, b), c) f(a, f(b, c)) for all a, b and c in S. Many also have identity elements and inverse elements.
Let B be a non-empty set with two binary operations+ and., a unary operation‘ and two distinct elements 0 and 1.
This cipher method is highly optimized for basic binary operations, which any processor can execute quickly, though of course it will be outstripped by specialized hardware and drivers….
Subtraction(-), multiplication(×), and division(÷) can be binary operations when defined on different sets, as are addition and multiplication of matrices, vectors, and polynomials.
However, both in universal algebra and model theory the binary operations considered are defined on all of S× S. Sometimes, especially in computer science, the term is used for any binary function.
Elemental binary operation.
However the binary operation might not be associative.
Non-register as LHS of binary operation.
Invalid operands in binary operation.
So, the statement"a group is a combination of a set S and a binary operation'*'" is already saying that the operation is closed.
A group is a combination of a set S and a binary operation'*' with the following properties.
A quasi-group satisfies a requirement that any element can be turned into any other by either a unique left-multiplication or right-multiplication;however the binary operation might not be associative.
Note that the dot product of two vectors is not a binary operation, external or otherwise, as it maps from S× S to K, where K is a field and S is a vector space over K.