Examples of using Codomain in English and their translations into Portuguese
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Colloquial
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Medicine
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Ecclesiastic
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Ecclesiastic
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Computer
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Official/political
Thus, it may not coincide with its codomain.
The codomain of a function is some arbitrary set.
An endofunction is a function whose domain is equal to its codomain.
The codomain of the curve is called trace of the curve.
Older books, when they use the word"range",tend to use it to mean what is now called the codomain.
Equipped with a codomain consisting of a discrete set of values.
An alternative definition of function by Bourbaki, namely as just a functional graph,does not include a codomain and is also widely used.
Note that the domain and codomain are in fact part of the information determining a morphism.
Among endofunctions on S one finds permutations of S andconstant functions associating to every x∈ S the same c∈ S. Every permutation of S has the codomain equal to its domain and is bijective and invertible.
If the codomain of a multilinear map is the field of scalars, it is called a multilinear form.
A function that is not surjective has elements y in its codomain for which the equation f(x) y does not have a solution.
In this case, the codomain of"f" must be specified, but is often assumed to be the set of all real numbers.
A constant function on"S", if"S" has more than 1 element,has a codomain that is a proper subset of its domain, is not bijective and non invertible.
In this case, its codomain is the set of real numbers formula_2, but its image is the set of non-negative real numbers formula_3, since formula_4 is never negative if formula_5 is real.
In 1978, quine([28]) presented a global theorem for stable applications between closed and oriented surfaces,which relates the sum of the degree of the cusps with the euler characteristic of the codomain and two sets of the application: one formed by the closure of regular regions that have preserved by the application and orientation, the other, formed by the closure of regular regions which has inverted orientation.
For this function, the codomain and the image are the same(the function is a surjection), so the word range is unambiguous; it is the set of all real numbers.
To ensure output distinguishability, the codomain of a function φ may be extended with special test outputs that are only relevant during testing.
The codomain is part of a function f if it is defined as described in 1954 by Nicolas Bourbaki, namely a triple(X, Y, F), with F a functional subset of the Cartesian product X× Y and X is the set of first components of the pairs in F the domain.
That is, a null function is an identity function whose domain and codomain are both the state space S of the program, and for which: f(s) s for all elements s in S. Less rigorous definitions may also be encountered.
The collection of monomorphisms with codomain"A" under the relation≤ forms a preorder, but the definition of a subobject ensures that the collection of subobjects of"A" is a partial order.

