I have a homework problem asking me to prove that it's impossible to construct a set of integers so that the set has certain characteristics. I've showed the following things:
- It's impossible to construct a set of integers modulo 100 so that the set has the required characteristics.
- Any set of integers with the required characteristics cannot contain two integers which are equivalent modulo 100.
How do I conclude the target assertion from these two facts? I would probably get full credit if I played the "clearly" card, but it isn't really clear (to me). Is there some simple proof by contradiction here which I'm not seeing?