Timeline for Is the set of real numbers really uncountably infinite?

9 events

when toggle format	what		by	license	comment
May 11, 2015 at 1:54	comment	added	rondo9		This is a really good question to ask!
May 11, 2015 at 1:18	answer	added	Qiaochu Yuan		timeline score: 4
May 10, 2015 at 20:01	comment	added	Priyanshu		Thanks Lucian! I understand the issue with the proof now.
May 10, 2015 at 19:50	comment	added	Priyanshu		Thanks Matt. Well I would have appreciated a more mathematical explanation of what exactly is wrong with what I mentioned. I'm totally convinced that the set of rational numbers is countably infinte and that the set of real numbers is not.
May 10, 2015 at 19:49	comment	added	Lucian		each number on the list has a finite length - Not all rationals have finite length.
May 10, 2015 at 19:13	comment	added	Matt Samuel		It's not possible to fix the proof because what you are trying to prove is not true. I promise nobody has been lying to you, the rationals are countably infinite and hence can be written in a list, but the set of reals is uncountable and cannot.
May 10, 2015 at 19:06	comment	added	Priyanshu		Thanks Daniel! Is it possible to address this by explicitly stating that each number on the list has non-zero digits till the $n^{th}$ place beyond which it can simply be appended with zeros i.e. each number on the list has a finite length. Not sure if this would lead to another flaw in the proof.
May 10, 2015 at 18:50	comment	added	Daniel Fischer		You don't know that the number you constructed is rational.
May 10, 2015 at 18:49	history	asked	Priyanshu	CC BY-SA 3.0