My Math Forum Which of the following is a better proof?

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 November 11th, 2017, 09:39 AM #1 Newbie   Joined: Oct 2017 From: Here Posts: 19 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...equence-of-rat 2) https://math.stackexchange.com/quest...l-numbers-such Each of the proofs I am referring to is the top answer on each link (marked with green V) Thanks
 November 11th, 2017, 02:00 PM #2 Global Moderator   Joined: May 2007 Posts: 6,581 Thanks: 610 The second one looks better to me. Thanks from Mathmatizer
 November 11th, 2017, 02:13 PM #3 Newbie   Joined: Oct 2017 From: Here Posts: 19 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, 01:03 PM   #4
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Quote:
 Originally Posted by Mathmatizer 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
(m+1)/n≥a requires a proof that there is a positive integer (m+1) meeting the requirement.

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