Yet another thread.. please bear with me... Dedekind question
Sorry i have no teacher so this is the only place i can get help. Btw i got another question about the Dedekind cut, i don't really understand what i need to do. It says : Using properties (A)-(H)
(In my book this is the basic properties of real numbers like commutative, associative,distributive laws.... the inverse of a number and the tricotomy property and transitive property ) of the real numbers and taking Dedekind theorem ( As stated in the previous question i posted) as given, show that every nonempty set U of real numbers that is bounded above has a supremum.
The hint is : Let T be the set of upper bounds of U and S be the set of real numbers that are not upper bounds of U.
What do i do? I mean i guess i can't use the completeness axiom. So how to i arrive at this result using only the basic properties of the real numbers and the Dedekind cut ? Btw Siclar
I don't understand what you mean when you say " these cuts is to construct the real numbers partitions of the rational numbers". What do you mean by partitions of rational numbers ? From what i understand we cut an interval of real numbers into two and then show that they are both bounded ( at the cut location) either from above or below . Is that what you mean ?
Originally Posted by siclar