# Difference Between Codomain and Range (With Table)

Mathematics has always been fun for someone who has quite an interest in it. The subject has many branches such as – geometry, algebra, probability, statistics, topology, mathematical logic, number theory, foundation, and many more. The terms codomain and range are the two terms that are studied in the sets and comes under the branch of mathematical logic.

## Codomain vs Range

The main difference between Codomain and Range is that Codomain determines the possible collective values which will come out, whereas Range determines you the actual value which will come out as a result. Codomain is said to be simple integers, while Range is said to be only even integers.

Codomain is to be the possible values of the function but also affect the answer of the function. They are said to be simple integers and never have restrictions on the size of the sets in a function. Codomain for the notation of the triple function: (A BG) – A is the domain of the function f, B is said to be the Codomain, and G is its graph.

The range is said to be the exact possible values of a y function but never affect the result of the function. The range is considered to be only the even integers. If we make changes in the values of the domain, then the values of the range also change concerning it.

## What is Codomain?

In Mathematics, there are many terms related to the sets that are important to know, and Codomain is among them. It doesn’t have an elaborate explanation but still can be distinguished slightly from the other terms.

To define what is codomain-it can be stated as the possible values of the given function, which will come out as a result of the respective equation. Codomain is simply integers that have no restrictions on the size of the set value. Codomain is sometimes referred to as the definition of the function.

Any changes in the domain will not change codomain, meaning if the domain values are changed, then it will not affect the possible values of the codomain, which will come out as a result. Also, it has been seen that the values of the codomain restrict the output of the given function, and the codomain is said to be the “mapping to” of the function from the domain.

## What is Range?

The word Range is used for wider meanings. It may be used in statistics and has an entirely different meaning. And it does mean the difference between the higher and the lower values of the given set of data. While it meant the difference for the range of the function, that is, it gives you all the possible values coming out as a result.

For a given function, there is only one range, which does not restrict the output of the function of the given equation. And is also known as the image of the function. The size of the set of the range is either equal or smaller than the size of the set of the codomain of the set.

The Range is also considered to be the subset of the codomain, and any changes in the values of the domain affect the values of the range. Unlike Codomain, the Range is not a mapping from the domain. It is just the image of all the value that comes out in codomain. It is believed that the range is only the outputted values and does not have any effect.

## Main Differences Between Codomain and Range

1. Codomain can be defined as the set of the possible values of a function, while Range can be defined as the most accurate value of a function.
2. Codomain can also be known as the definition of a function, whereas the Range is also known to be the image of a function.
3. It is found that codomain can restrict the output of the function while it is contrasting for the Range as it does not restrict the output of the function.
4. For Codomain, the size of the set is not defined; therefore, no restrictions at all, whereas for Range, the size of the set is said to be equal to or smaller than the codomain set.
5. Codomain has a direct effect on the answer, while the Range does not play this important role and thus, does not affect the answer.

## Conclusion

The above two topics are related to mathematics. Both the terms are although different from each other and slightly dependent on one another, but pointing out the difference in two is a major work as both the terms have the slightest difference and only be distinguished by someone who is a keen lover or expert of mathematics.

Codomain was talking about the exact possible value and is also known to be the definition of the function. It does restrict the output of the function. Also, codomain does not have any size specified for the sets of the function, and any changes in codomain directly affect the answer.

Contrastingly, not restricting the output and oppositely restricting the size of set Range talks about the possible values and not the exact one like Codomain. And is also known as the image of the function.

1. https://ijmmu.com/index.php/ijmmu/article/view/1818
2. https://iopscience.iop.org/article/10.1088/1742-6596/1657/1/012073/meta
3. https://www.sciencedirect.com/science/article/pii/S0304397515003151
4. https://www.sciencedirect.com/science/article/abs/pii/S0306261919305446