The discussion revolves around proving a bijection between the sets (X^Y)^Z and X^(Y x Z), where X and Y are sets and Z is another set. The participants are exploring the nature of functions and ordered pairs within these set constructions.
The discussion is active, with participants engaging in clarifying the definitions and properties of the sets involved. Some guidance has been offered regarding the interpretation of elements in the sets, but there is no explicit consensus yet.
Participants express confusion about the initial steps needed to approach the proof, indicating a potential gap in understanding the foundational concepts of set functions and bijections.
No. It would be a function from Z to X^Y, right? So for each zεZ it would pick out a function from Y to X. And if you supply that function with an element of Y it will give you an element of X. So in total, giving that function from Z to X^Y both an element of Z and an element of Y you find an element of X. Do you see it now?bedi said:Its elements are the ordered pairs (z,(y,x)) aren't they?