The addition of Dedekind cuts is defined as the sum of the elements (r+s) with r in A and s in B. However, the sets are closed downwards and there is no largest element in the set...so how do you know what to add?(adsbygoogle = window.adsbygoogle || []).push({});

For example, the cut for 2 added to the cut of 3 should equal the cut of 5. so we should obtain all the rationals to the left of 5. However, what element in the cut for 3 is added to say 1 in the cut of 2 to obtain a corresponding element in the cut of 5? I mean I guess all you have to do is add the 3 and the 2 and just say that you have all the elements to the left of 5..but i dont think this method would work for adding the Dedekind cuts of irrationals without explicitly defining irrationals before hand which would seem to defeat the purpose...like the cut for √2 added to the cut for √5 is the cut of √2+√5 ...but I feel like that assumes that the reals have already been constructed.

Also, does anyone know if Dedekind cuts can be used to prove that pi is irrational...for that matter does anyone know the Dedekind cut representation of pi?

-Thanks for your time

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# Question about the sum of Dedekind cuts

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