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 December 3rd, 2017, 08:42 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, 09:53 PM   #2
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 Originally Posted by Antoniomathgini 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.
If you figured out sqrt(3) then adding 2 should be easy. What do you mean by 6i?

 December 4th, 2017, 11:48 AM #3 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894 The square root of three can be written as the Dedekind cut consisting of all negative rational numbers together with all non-negative 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 non-negative 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. Thanks from Antoniomathgini Last edited by Country Boy; December 4th, 2017 at 11:54 AM.

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