Hi All, this shouldn't take anyone worth their salt too long.... i'm just wondering if this is correct:
If the task is to prove that:
is a bijection from onto ...
Do we go about it this way?
To show injectivity:
Assume there exists such that: and also that .
Isolating in the first equation, we can sub in to the second to get and then we can repeat the similar process, just isolating to arrive at ?
Then to show surjectivity:
Do we just pick any in . We set and then solve for and in terms of and . I get and ??