Prove that the set of all dedekind cuts is uncountably infinite.

Its fairly straightforward to prove that the power set of the rational numbers is uncountably infinite. However, the set of all dedekind cuts is a proper subset of the power set of all rational numbers. Not all proper subsets of the power set of all rational numbers are uncountable.

Assume that the definition of real numbers is dependent upon dedekind cuts, therefore you cannot use the uncountability of the real numbers as a proof of the uncountability of the set of all dedekind cuts, as such a proof would be circular logic.

better question!
is anyone familiar with F-testing in statistics? :p
more specifically, determining whether differences in frequency data between subgroups are statistically significant?

if so, msg me :p

i'd probably get an F on a test in statistics, pang. does that count?

@ Rockman - The answer is 42

@ Pang - The answer is also 42


Next Question...

I think Dedly and I had the same math teacher.

Pang, if you were on IRC I could tell you

i remember touching on f-testing at uni, but i can positively guarentee i have completly forgotten it.

Circular logic is the most popular logic today, so why is it not acceptable? It's used by politicians, religious people, economists. I think only engineers sometimes try something else. So why not use it?

@pang yes.
why..

i thought the dedekind was exinct. or was that the dodokind, dang e's and o's are confusing.

Rockman, the solution is fairly obvious. As you can't rely on the uncountability of rational numbers, you must prove an both an infinite number of power sets and an infinite number of dedekind cuts. However, that doesn't show uncountability.

That comes in where you use (A, B) and (C, D), where subset (A, B) is lower than subset (C,D) and B is lower than C. As A is lower than C, you have an a power set of cuts generated with every subsequent set beyond D.

Pang, determine your level of significance, then calculate F as (between group variability)/(witin group variability). If that F exceeds the F-critical, then it is statistical significant.