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 2015-09-16, 13:22 #45 wildrabbitt   Jul 2014 2·32·52 Posts I've finished the proof of lemma 1 in my head. I will write it down now and post it as soon as.
 2015-09-16, 13:39 #46 LaurV Romulan Interpreter     "name field" Jun 2011 Thailand 3·23·149 Posts Can you $\TeX$? It saves time, easy to make corrections, easy for other to read or copy, etc... You can preview interactively to see if it appears as you intended. Just suggestion, no harm intended. No harm if you can't. edit: induction? Last fiddled with by LaurV on 2015-09-16 at 13:44 Reason: s/save/saves/
 2015-09-16, 14:36 #47 wildrabbitt   Jul 2014 1110000102 Posts If you'll give me a couple of days max to prove my lemma I'll learn to TEX. Deal?
 2015-09-16, 14:42 #48 wildrabbitt   Jul 2014 2·32·52 Posts Actually I think I do have it. Hang on.
2015-09-16, 15:47   #49
axn

Jun 2003

10101001111012 Posts

Quote:
 Originally Posted by wildrabbitt If you'll give me a couple of days max to prove my lemma I'll learn to TEX.
What's the rush? Take your time.

 2015-09-16, 20:03 #50 wildrabbitt   Jul 2014 2×32×52 Posts Okay. Thanks for waiting. I've finished the proof. The rest of the whole proof is easy. I am certain I can show that all the series of reciprocals formed from any set of positive integers with no a.p's longer than 2 converges and is bounded above by the number 6. Here's the beginning : I understand it's quite hard work reading a long proof. I hope some of you will make the effort because it's correct. Haven't had time to learn TEX but I guess you're okay about that (for now) and I can only post two pages at once. http://www.mersenneforum.org/attachm...1&d=1442433731 http://www.mersenneforum.org/attachm...1&d=1442433740 Attached Thumbnails
 2015-09-16, 20:09 #51 wildrabbitt   Jul 2014 1C216 Posts This might help to visualise the issue : http://www.mersenneforum.org/attachm...1&d=1442434165 Attached Thumbnails
 2015-09-16, 20:17 #52 wildrabbitt   Jul 2014 2×32×52 Posts Attached Thumbnails
2015-09-16, 20:41   #53
VBCurtis

"Curtis"
Feb 2005
Riverside, CA

160616 Posts

Quote:
 Originally Posted by R.D. Silverman Actually, for a non-native speaker, your English is SUPERB.
This is one of the nicest things RDS has said all year. Congrats, LaurV!

2015-09-17, 01:55   #54
LaurV
Romulan Interpreter

"name field"
Jun 2011
Thailand

240518 Posts

Quote:
 Originally Posted by VBCurtis This is one of the nicest things RDS has said all year. Congrats, LaurV!
Quote:
 Originally Posted by R.D. Silverman Actually, for a non-native speaker, your English is SUPERB.
Yeah, thanks a lot Mr. Silverman, unfortunately it is not true, and also unfortunately, it is not about math...
Dreaming of the day when you will say "your number theory is satisfactory", haha, most probably never
/end of offtopic

Last fiddled with by LaurV on 2015-09-17 at 01:58

 2015-09-17, 17:13 #55 wildrabbitt   Jul 2014 2×32×52 Posts I feel it's my duty in case the lack of responses so far isn't because everyone's lost interest, to post the rest of the proof of the lemma. There's still one more to page to come after these and after that there's a little more about the density of the terms of the sequence of positive integers. I'll post the rest of this lemma's proof but I won't post anymore after that unless people say they want me to. http://www.mersenneforum.org/attachm...1&d=1442509786 http://www.mersenneforum.org/attachm...1&d=1442509786 Attached Thumbnails

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