- #1
hitmeoff
- 261
- 1
Homework Statement
Show that if [tex]\alpha[/tex] and [tex]\beta[/tex] are Dedekind cuts then so is [tex]\alpha[/tex] + [tex]\beta[/tex]={r1+r2: r1 [tex]\epsilon[/tex] [tex]\alpha[/tex] and r2[tex]\epsilon[/tex][tex]\beta[/tex]
Homework Equations
The Attempt at a Solution
If a dedekind cut is a cut whereby the sets on the left side of the cut and the right side of the cut would contain all the rational numbers then the cut itself is an irrational number right? If you add to irrationals don't you get another irrational number, thereby having another cut where the LH U RH still contains all the rationals?