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I couldn't understand what mapping and mapping diagrams (in context of functions), i searched many websites and listened to many videos but the explanations i got from them were in conflict with each other. Most of them said mapping is a rule or operation but if mapping is a rule or operation how can there be different types of rule or operation(types of mapping). And few of them said mapping is representation of a function but if mapping is a representation then what does mapping diagram means. And other few of them said function is a type of mapping (assuming mapping is rule or operation). I am really confused. Could anybody help me please? I need some assistance.

Mauro ALLEGRANZA
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Daniel Joseph
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  • I've never heard the term "mapping diagram", but a google search shows that it means a pictorial realization of a function, or a mapping, between two finite sets. As to the difference between function and mapping, people aren't entirely consistent there. Some people require a function to take values in $\mathbb R$ or $\mathbb C$ or at least some field. Others (myself, for instance) allow mappings to be multivalued. See, e.g., this question. Context ought to clarify an author's intent. – lulu Mar 04 '22 at 15:32
  • Ought to have said, as the question I linked to suggests, some people treat "function" and "mapping" as synonyms. – lulu Mar 04 '22 at 15:34
  • Map (mathematics): a map is often used as a synonym for a function. – Mauro ALLEGRANZA Mar 04 '22 at 16:11
  • @lulu- I read the all the answers for the linked question but real analysis and differential geometry is too advanced for me. I also saw that the first answer said function and mapping were different terms used for the same mathematical object. The book that i read gave the definition of mapping as "a rule that relates one set of items or numbers to another" and moment i got confused is when they gave a diagram and said that the diagram shows the mapping. How can mapping be both a rule and diagram? and i got more confused when they said there were different types of mapping. – Daniel Joseph Mar 05 '22 at 03:29
  • A small correction in the fourth line in my previous comment " and the moment i got confused is when they ....." – Daniel Joseph Mar 05 '22 at 03:45

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