December 3rd, 2017, 09:42 PM  #1 
Member Joined: Apr 2017 From: Canada Posts: 32 Thanks: 2  Dedekind Cuts :(
6. How do you define sqrt(3) + 2 as a Dedekind cut? 6i. How do we define addition in 2? I've figured out that the Dedekind cut for sqrt(3), but the addition of 2 throws me off. 
December 3rd, 2017, 10:53 PM  #2 
Senior Member Joined: Aug 2012 Posts: 2,427 Thanks: 760  If you figured out sqrt(3) then adding 2 should be easy. What do you mean by 6i?

December 4th, 2017, 12:48 PM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
The square root of three can be written as the Dedekind cut consisting of all negative rational numbers together with all nonnegative rational numbers, x, such that $x^2< 3$. The Dedekind cut corresponding to square root of three plus two is the set of all negative number together with all nonnegative rational numbers, x, such that $(x 2)^2< 3$. I don't know what you mean by "addition in 2". Did you mean "addition in R", that is, addition of Dedekind cuts? If so the Dedekind cut corresponding to x+ y, where x and y are Dedekind cuts is just the set, {a+ b} where a is a rational number in x and b is a rational number in y. Last edited by Country Boy; December 4th, 2017 at 12:54 PM. 

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