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I define an overloaded function, for instance as follows:

$$f: \mathbb{Set}_1 \rightarrow \mathbb{Set}_3$$ $$f: \mathbb{Set}_2 \times \mathbb{Set}_2 \rightarrow \mathbb{Set}_3$$

My first question is whether it is appropriate to define an overloaded function in math, which has no problem in some programming languages of computer science.

My second question is, as there is no intersection between $\mathbb{Set}_1$ and $\mathbb{Set}_2 \times \mathbb{Set}_2$, if it is allowed to simply the notation like that:

$$f: (\mathbb{Set}_1 \uplus (\mathbb{Set}_2 \times \mathbb{Set}_2)) \rightarrow \mathbb{Set}_3$$

Could anyone help? Thank you very much.

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    I suppose you could do that, but in pure math it's prudent to just define distinct functions instead of overloading one. I'm not sure what your applications are or whatever though.2011-08-09

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