Codomain is an English word. Below you'll find 10+ example sentences showing how it's used in practice.
Codomain in a sentence
Codomain meaning
- The target set into which a function is formally defined to map elements of its domain; the set denoted Y in the notation f : X → Y.
- The set B.
Using Codomain
- The main meaning on this page is: The target set into which a function is formally defined to map elements of its domain; the set denoted Y in the notation f : X → Y. | The target set into which a function is formally defined to map elements of its domain; the set denoted Y in the notation f : X → Y. | The set B.
- In the example corpus, codomain often appears in combinations such as: the codomain, and codomain, codomain is.
Context around Codomain
- Average sentence length in these examples: 30.5 words
- Position in the sentence: 3 start, 11 middle, 2 end
- Sentence types: 16 statements, 0 questions, 0 exclamations
Corpus analysis for Codomain
- In this selection, "codomain" usually appears in the middle of the sentence. The average example has 30.5 words, and this corpus slice is mostly made up of statements.
- Around the word, whole, equal and set stand out and add context to how "codomain" is used.
- Recognizable usage signals include and a codomain set that and and the codomain are topological. That gives this page its own corpus information beyond isolated example sentences.
- By corpus frequency, "codomain" sits close to words such as aaaa, abductees and abdulahi, which helps place it inside the broader word index.
Example types with codomain
The same corpus examples are grouped by length and sentence type, making it easier to see the contexts in which the word appears:
Every permutation of S has the codomain equal to its domain and is bijective and invertible. (16 words)
Examining the differences between the image and codomain can often be useful for discovering properties of the function in question. (20 words)
In other words, every element of the function's codomain is the image of at most one element of its domain. (21 words)
If the codomain (-π/2, π/2) was made larger to include an integer multiple of π/2 then this function would no longer be onto (surjective) since there is no real number which could be paired with the multiple of π/2 by this arctan function. (47 words)
A relation from a domain A to a codomain B is a subset of the Cartesian product A × B. Given this concept, we are quick to see that the set F of all ordered pairs (x, x 2 ), where x is real, is quite familiar. (45 words)
Formal definition Given a function f:X→Y, the set X is the domain of f; the set Y is the codomain of f. In the expression f(x), x is the argument and f(x) is the value. (39 words)
Example sentences (16)
Examples A non-surjective function from domain X to codomain Y. The smaller oval inside Y is the image (also called range ) of f. This function is not surjective, because the image does not fill the whole codomain.
A relation from a domain A to a codomain B is a subset of the Cartesian product A × B. Given this concept, we are quick to see that the set F of all ordered pairs (x, x 2 ), where x is real, is quite familiar.
Every permutation of S has the codomain equal to its domain and is bijective and invertible.
Examining the differences between the image and codomain can often be useful for discovering properties of the function in question.
Formal definition Given a function f:X→Y, the set X is the domain of f; the set Y is the codomain of f. In the expression f(x), x is the argument and f(x) is the value.
If the codomain (-π/2, π/2) was made larger to include an integer multiple of π/2 then this function would no longer be onto (surjective) since there is no real number which could be paired with the multiple of π/2 by this arctan function.
In other words, every element of the function's codomain is the image of at most one element of its domain.
Instead of using the areas of rectangles, which put the focus on the domain of the function, Lebesgue looked at the codomain of the function for his fundamental unit of area.
It has a domain set R and a codomain set that is also R, because the set of all squares is subset of the set of all reals.
Occasionally, a partial function with domain X and codomain Y is written as f: X ⇸ Y, using an arrow with vertical stroke.
Some transformations may have image equal to the whole codomain (in this case the matrices with rank 2 ) but many do not, instead mapping into some smaller subspace (the matrices with rank 1 or 0 ).
The composition of any two elements of G exists, because the domain and codomain of any element of G is A. Moreover, the composition of bijections is bijective ; Wallace, D. A. R., 1998.
The function associating to each natural integer n the floor of n/2 has its image equal to its codomain and is not invertible.
The logarithm of a non-positive real is not a real number, so the natural logarithm function doesn't associate any real number in the codomain with any non-positive real number in the domain.
The term one-to-one function must not be confused with one-to-one correspondence (aka bijective function ), which uniquely maps all elements in both domain and codomain to each other, (see figures).
This definition does only require that the domain and the codomain are topological spaces and is thus the most general definition.
Common combinations with codomain
These word pairs occur most frequently in English texts:
- the codomain 6×
- and codomain 5×
- codomain is 3×
- codomain of 3×
- to codomain 2×
- whole codomain 2×