How many mappings are there for a finite set of elements?

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Homework Help Overview

The discussion revolves around determining the number of mappings for a finite set of elements, specifically focusing on mappings of a set S into itself. The original poster seeks clarification on the total number of mappings based on the number of elements in the set.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants explore the implications of different types of mappings, including constant and surjective mappings. There is a discussion on whether the original poster's understanding of the number of mappings is complete, with some questioning the assumptions made about the nature of the mappings.

Discussion Status

The discussion is active, with participants providing insights into the nature of mappings and raising questions about the original poster's assumptions. Some guidance has been offered regarding the counting principles applicable to the problem, but no consensus has been reached on the exact number of mappings.

Contextual Notes

There is a lack of specificity regarding the definitions of the types of mappings being considered, such as surjective or injective mappings. The original poster's phrasing may lead to different interpretations of the problem.

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If S is a finite set having m > 0 elements, how many mappings are there of s into itelf?



I believe there would be however many mappings there are elements> Any suggestions?
 
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I believe there would be however many mappings there are elements

Consider the mapping where every element maps to one particular element (i.e. the constant map). You didn't specify a surjective map that I can tell, so the possibilities are much larger than you currently think.
 


That is the question as to how it is written. Am I anywhere close.
 


There are more mappings than you have indicated that are surjective, much less not surjective. How many do you think there are that map distinct elements to distinct elements? There are way more than m.
 


If your set has n members, then you can map the first into any of those n members: you have n choices. The same is true of the second member, etc.

"Fundamental Counting Principle": If you have n choices for A and n choices for B then you have mn choices for A and B.
 

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