
Math General Math Forum  For general math related discussion and news 
 LinkBack  Thread Tools  Display Modes 
December 14th, 2015, 03:14 PM  #11  
Math Team Joined: Dec 2013 From: Colombia Posts: 7,599 Thanks: 2587 Math Focus: Mainly analysis and algebra  Quote:
In any nonempty interval there are infinitely many ($\aleph_0$) rationals and infinitely many ($\mathfrak c$) reals. It doesn't matter whether the endpoints are rational, irrational or one of each.  
December 14th, 2015, 03:17 PM  #12 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,599 Thanks: 2587 Math Focus: Mainly analysis and algebra  Yes, this is very basic stuff. You should also be aware that we cannot prove that $\mathfrak c=\aleph_1$. That is: it has been proved that we cannot prove it. It is formally undecidable.


Tags 
cardinality, continuous, continuum, continuum hypothesis, hypothesis, set 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
A word in favor of Continuum Hypothesis  hofhile  Applied Math  10  May 25th, 2014 01:38 PM 
Represent continuum betw summary and detail of timed neural  BenFRayfield  Number Theory  0  January 19th, 2014 08:02 PM 
Disproof of Continuum Hypothesis  cardinality is continuous  BenFRayfield  Number Theory  4  May 23rd, 2013 05:58 AM 
Questions on infinities order and Continuum hypothesis.  Eureka  Applied Math  6  November 22nd, 2011 09:55 AM 
Proving that a space is continuous, continuous at 0, and bdd  thedoctor818  Real Analysis  17  November 9th, 2010 09:19 AM 