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I need to prove the following:
For a, take a step back. Look at what it is saying. Don't see 2n and don't see -2n+1. See odd and even. Now it should become clear, that all that the map is a bijection since all evens and all odds are hit, and only positives go to evens and only negatives go to odds.
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."