Can you construct uncountable set from countable sets?

msg908 · June 21st, 2006, 7:03 am

Hi,Can you construct an uncountable set from countable sets?Any thoughts?Msg.

zarnywhoop · June 21st, 2006, 7:07 am

Set of subsets of the integers.

DavidJN · June 21st, 2006, 11:19 am

The question makes me think of Godels Incompleteness Theorem.

N · June 21st, 2006, 11:40 am

No, all countable sets have cycles.

elan · June 21st, 2006, 11:57 am

QuoteOriginally posted by: DavidJNThe question makes me think of Godels Incompleteness Theorem.I bet the thought is: we will never know the answer to this question...

vixen · June 21st, 2006, 12:26 pm

zarnywhoop is correct.The set of subsets of integers cannot be put into one-to-one correspondence with the set of integers.

N · June 21st, 2006, 12:54 pm

QuoteOriginally posted by: vixenzarnywhoop is correct.The set of subsets of integers cannot be put into one-to-one correspondence with the set of integers.V, You need to take a year out of your busy life and teach a course in Topos theory.N

vixen · June 21st, 2006, 1:28 pm

QuoteOriginally posted by: NQuoteOriginally posted by: vixenzarnywhoop is correct.The set of subsets of integers cannot be put into one-to-one correspondence with the set of integers.V, You need to take a year out of your busy life and teach a course in Topos theory.Nyou mean.... take a course in Topos theory, right?

Collector · June 21st, 2006, 1:44 pm

easy: Donate all your money: now your countable set is gone!All the love? you receive from the donation how do you count that? You have constructed a uncountable set from a countable! Most people these days seems to prefer to go the other way around: exchanging uncountable sets and get back countable sets (money).... Only people that also know how to count uncountable sets lives in full harmony! A course in Topos theory is probably a step in the right direction for many Geeks! N: "No, all countable sets have cycles."True: money always moves in boom-busts cycles!

CactusMan · June 21st, 2006, 2:25 pm

This is a basic math question. Doesn't really belong here, right? Why ask this here?What methods of construction are you allowing? If you are allowing taking subsets, then this is well know, right? Collection of all subsets of the integers is uncountable.But, what's the point of asking this here?

Collector · June 21st, 2006, 3:00 pm

CactusMan this is brilliant:So now you try to count if this question should be countable under this forum or not

vixen · June 21st, 2006, 3:06 pm

So now you try to count if this question should be countable under this forum or not This is Godel undecidable within this thread!

Cuchulainn · June 21st, 2006, 8:22 pm

QuoteYou need to take a year out of your busy life and teach a course in Topos theory.Since this thread is becoming silly, I advise, not Topos but take a course in Accounting. Then everything becomes countable.

msg908 · June 22nd, 2006, 1:34 am

Isn't Godel the one who says that you can't really prove anything?msg.

zarnywhoop · June 22nd, 2006, 7:23 am