>>36
I think I'm fine with that proof. It's a very useful property used in many proofs, but it doesn't seem to be what the Wikipedia article linked earlier in the thread claims. The Wikipedia article bases its claim beyond those I gave on the idea that infinities and infinitesimals are incomparable, which I'm fairly certain all non-standard analysis reject. The textbook I used never claimed that infinitesimals and infinities were impossible due to the Archemidean property.