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what is the basic difference between a mapping and a function? many say they are same but the opposite views are also seen. is mapping a restricted version of a function?

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Probably most modern texts would agree that there is no mathematical difference between function and mapping. Historically, and not a very long time ago, and in difference disciplines the two were used to mean different things. For instance, in topology and metric space theory sometimes 'mapping' stands for 'continuous function'. In analysis it is common to speak of functionals, which are linear operators to the ground field. In that context 'function' may stand for a functional from the ground field (necessarily to the ground field), while 'mapping' stands for a continuous function. So, I'm afraid historically things are far from clear-cut. But again, the modern approach is very clear: both mean the exact same thing.

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  • $\begingroup$ then why we use the terms "single-valued function" or "multi-valued function"? $\endgroup$ Commented Nov 25, 2014 at 4:30
  • $\begingroup$ I'm not sure what that has to do with the question and/or answer. $\endgroup$ Commented Nov 25, 2014 at 4:33
  • $\begingroup$ *and. for a mapping, every elements in domain assigns uniquely to codomain.but for a multivalued function this property fails. so why should we call a mapping as function? plz clear $\endgroup$ Commented Nov 25, 2014 at 4:38
  • $\begingroup$ you seem to be asking a different question now. Who said anything about multi-valued anything? $\endgroup$ Commented Nov 25, 2014 at 4:51
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I think a map and function are usually synonymous amongst mathematicians. Often you will see "let $f$ be a map" or "let $f$ be a function" used interchangeably.

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