What makes 1-1 mappings special and why do we use them in mapping and functions?

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One-to-one mappings, or 1-1 functions, are defined as functions because they allow for a clear comparison between sets. These functions are special due to their invertibility, meaning that each output corresponds to a unique input, which is a desirable property in various fields of study. The ability to invert these functions enhances their utility in mathematical analysis and applications. This distinct characteristic sets them apart from many-one mappings, which do not provide the same level of clarity or functionality. Overall, the significance of 1-1 mappings lies in their ability to facilitate comparisons and ensure unique correspondences between elements.
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Mapping and functions...

Why do were define one-one and many-one mappings as functions? Why do we separate them into a different group and make them special?

Thanks in advance. :smile:
 
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1-1 functions allow us to compare sets. Also, 1-1 functions are invertible on the image of their domain. Invertibility is a "nice" feature in many areas of study.
 
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