- I'm working on this problem and I'm thinking about using contradiction. I'm not sure if this is the correct approach, and if it is, whether I've set it up correctly.
Main Question or Discussion Point
Ok, so here is what I have so far:
Suppose ##T_1## is infinite and ##\varphi : T_1 \rightarrow T_2## is a bijection.
I'm thinking I would then show that there is a bijection, which would be a contradiction since an infinite set couldn't possibly have a one-to-one correspondence with a finite set.
This idea makes sense to me logically and I'm pretty sure I can assume bijection since it's the "if" part of an if-then statement. I guess I'm just trying to figure out how to deduce that every element in ##T_1## corresponds with ##T_2## without making any logic jumps. That is if this is even a correct approach at all.
Any help is greatly appreciated, thank you!