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

  • Level: Graduate 
  • Thread starter Thread starter Gear300
  • Start date Start date
  • Tags Tags
    Mapping
Join the discussion
Registration is free. Start your own thread to ask a follow-up.
Sign up Log in
5 replies · 2K views
Gear300
Messages
1,212
Reaction score
10
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?
 
Physics news on Phys.org

Discussion



That's the defining property of a being a function from S to T.
 


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".