Proving that this set is a Dedekind cut.

[jdinatale]

Homework Statement

Homework Equations

In the above proplem, A is a dedekind cut.

To be a cut:
1. A \not= \mathbf{Q} and A \not = \emptyset
2. If r \in A, then all s \in A for all s \in \mathbf{Q} such that s < r
3. A has no maximum


I know the 3 properties by heart, but the set -A is so unwieldy, that I'm having difficulty proving each of these properties.

 

[Hurkyl]

Then try things step-by-step. First, carefully write out what it is to be proven, incorporating the definition of -A...