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November 11th, 2017, 10:39 AM   #1
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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)

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November 11th, 2017, 03:00 PM   #2
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The second one looks better to me.
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November 11th, 2017, 03:13 PM   #3
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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
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November 12th, 2017, 02:03 PM   #4
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Quote:
Originally Posted by Mathmatizer View Post
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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