Mathematics has always been fun for someone who has quite an interest in it. The subject has many branches: geometry, algebra, probability, statistics, topology, mathematical logic, number theory, foundation, and many more.

The terms codomain and range are studied in the sets and come under the branch of mathematical logic.

## Key Takeaways

- The codomain is the set of all possible output values of a function, while the range is the actual set of output values produced by the function.
- The codomain is determined by the nature of the function and its definition, while the input values of the function determine the range.
- The codomain is always equal to or larger than the range, but the range may be a proper subset of the codomain.

**Codomain vs Range**

In mathematics, Codomain determines the possible collective values which will come out. The range is the set of actual output values produced by the function. Codomain is said to be a simple integer, while Range is only an even integer.

Codomain is to be the possible values of the function but also affect the function’s answer. They are said to be simple integers and never have restrictions on the size of the sets in a process.

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 affects the result of the process. The content is considered to be only the even integers.

**Comparison Table**

Parameters of Comparison | Codomain | Range |
---|---|---|

Definition | Codomain is all possible sets of values resulting from a given function. | The Range is described as all the actual values of a function that will result. |

Also Known As | Codomain is also known as the definition of a function. | The Range is also known as the image of the function. |

Purpose | Co-domain restricts the output of the given function. | The Range does not restrict the output of the given function. |

Set Size | No restrictions | It is said to be equal to or smaller than the codomain set. |

Effect on Answer | It has a direct impact on the answer. | It does not have a direct effect on the answer. |

**What is Codomain?**

In Mathematics, many terms related to the sets are essential, and co-domain is among them.

To define 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.

Any changes in the domain will not change the 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.

**What is Range?**

The word Range is used for a broader meaning. It may be used in statistics and has an entirely different meaning. And it does mean the difference between the given data set’s higher and lower values.

For a given function, there is only one range, which does not restrict the output of the part of the given equation. And is also known as the image of the function.

The Range is also considered the subset of the codomain, and any changes in the domain’s values affect the range’s values. Unlike Codomain, the Range is not a mapping from the domain.

It is just the image of all the values in the codomain. The range is believed to be only the outputted values and has no effect.

**Main Differences Between Codomain and Range**

- 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 process.
- Codomain can also be known as the definition of a function, whereas the Range is also known to be the image of a function.
- It is found that codomain can restrict the output of the function while contrasting for the Range as it does not limit the production of the function.
- 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.
- Codomain directly affects the answer, while the Range does not play this vital role and, thus, does not affect the answer.

**References**

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

Piyush Yadav has spent the past 25 years working as a physicist in the local community. He is a physicist passionate about making science more accessible to our readers. He holds a BSc in Natural Sciences and Post Graduate Diploma in Environmental Science. You can read more about him on his bio page.