I have a question that I'm stuck on.
It goes:
Let A, B be the following sets:
$A = \{1, 4, 9, …\} = \{n^2| n \in N\} $
$B = \{1, 16, 81, …\} = \{n^4| n \in N\} $
- Define a bijection between A, B.
- Define a non-bijection between A, B.
I know that a bijective function is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set.
So that for every $a \in A$ there is $b \in B$ so that $f(a)=b$
What do they mean by "Define"? I can't seem to understand what I need to do in this question.
Sorry for my English and Thanks for the help!
Best Answer
You need to give an explicit example of a bijection between $A$ and $B$ and an explicit example of a non-bijection between these two sets.