I was given the following task
Define a bijection between ${(A^B)}^C$ and $A^{B \times C}$
I have no clue where to start and I don't understand the task. Could you please explain what I am required to show and how should I start the proof ?
Asked
Active
Viewed 228 times
0
Arctic Char
- 16,007
Rustem Sadykov
- 183
-
Ummm... what are $A$, $B$, and $C$? Don't you think that matters? – David G. Stork Sep 17 '20 at 05:08
-
This information was not given in the description of a task. – Rustem Sadykov Sep 17 '20 at 05:13
1 Answers
0
For sets, $A^B$ represents the set of functions from $B$ to $A$. That means $(A^B)^C$ is the set of functions from $C$ to (functions from $B$ to $A$). $A^{B \times C}$ is the set of functions from $B \times C$ to $A$. You are expected to describe a bijection between these sets.
Ross Millikan
- 374,822
-
Right, so to describe bijection, I have to show that $f$ is 1-1 and onto. Could you suggest how should I start? – Rustem Sadykov Sep 17 '20 at 05:16
-
Think of what the functions look like. There is a very natural bijection between them. – Ross Millikan Sep 17 '20 at 13:55