What to choose for co-domain, somewhat confused

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In summary, when choosing a co-domain for a function, it can be any space that is greater than the range or image. This could include R^2, R^3, etc. On the other hand, the range or image is a subset of the co-domain, such as R^+ (all positive reals). The co-domain is the space that the function maps to, while the range is what actually comes out. Examples of co-domains can be found on the Wikipedia page for "Codomain."
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When you choose the co-domain can it just be anything that is greater than the range (i.e. the image)? In general, should the co-domain just be whatever space it maps to: R^2, R^3, etc. whereas the range is a subset of that space such as R^+ (all positive reals)?
 
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Yes, the codomain is the space that the function maps to - that is, all the possible outcomes. This is usually given in the definition of the function. The image/range is what actually comes out. The wikipedia page for http://en.wikipedia.org/wiki/Codomain" has some examples
 
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Related to What to choose for co-domain, somewhat confused

1. What is a co-domain in mathematics?

A co-domain is the set of all possible outputs or values that a function can produce.

2. How do I choose a co-domain for a function?

The co-domain should be chosen based on the range of values that the function can produce. It should be large enough to encompass all possible outputs of the function.

3. Can the co-domain be smaller than the range of a function?

No, the co-domain must be at least as large as the range of the function. Otherwise, there will be elements in the range that have no corresponding output in the co-domain.

4. What is the difference between a co-domain and a range?

The co-domain is the set of all possible outputs of a function, while the range is the set of actual outputs that the function produces for a given set of inputs.

5. How does choosing a co-domain affect the function?

The co-domain does not affect the behavior of the function. It simply determines the set of values that the function can produce.

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