Mapping a: S -> T be so that any x ε S has one and only one y &#

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A mapping a: S --> T is defined such that for every element x in set S, there is one and only one corresponding element y in set T. This property is essential for a mapping to be classified as a function. The necessity of this condition arises purely from the definition of a function, rather than from any broader context. Discussions indicate that while functions adhere to this rule, there are mappings that do not qualify as functions. Clarifying the specific sets S and T can further enhance understanding of the topic.
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mapping a: S --> T be so that any x ε S has one and only one y &#

What makes it necessary for any mapping a: S --> T be so that any x ε S has one and only one y ε T?
 
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That's the defining property of a being a function from S to T.
 


So it is necessary only by definition?
 


It is not necessary at all. One can talk about mappings that are not functions as well. What is the context of this question?
 


I see...what I was referring to were particular types of mappings (functions), right?
 


It might help if you told us exactly what you mean by "S" and "T"!

If you are referring to any sets S and T and by "mapping" you specifically meant "function", then yes, that is true simply because of the definition of "function".
 

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