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November 11th, 2017, 10:39 AM  #1 
Newbie Joined: Oct 2017 From: Here Posts: 13 Thanks: 0  Which of the following is a better proof?
I needed to prove that every real number is the limit of a convergent sequence of rational numbers, and I had hard times, so I looked it up online , I found 2 proofs online, but I'm not sure if both are correct mathematically. Which one do you suggest better, and has no mathematical errors? 1) https://math.stackexchange.com/quest...equenceofrat 2) https://math.stackexchange.com/quest...lnumberssuch Each of the proofs I am referring to is the top answer on each link (marked with green V) Thanks 
November 11th, 2017, 03:00 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,416 Thanks: 558 
The second one looks better to me.

November 11th, 2017, 03:13 PM  #3 
Newbie Joined: Oct 2017 From: Here Posts: 13 Thanks: 0 
Thanks, I just don't understand the first remark about "One really requires proof that there is a positive integer m such that m/n≥a."  where is it used? he only used (m+1)/n≥a, and not m/n≥a

November 12th, 2017, 02:03 PM  #4 
Global Moderator Joined: May 2007 Posts: 6,416 Thanks: 558  (m+1)/n≥a requires a proof that there is a positive integer (m+1) meeting the requirement.
