probabilistic number theory - Page 5

wildrabbitt · 2015-09-16, 13:22

I've finished the proof of lemma 1 in my head. I will write it down now and post it as soon as.

LaurV · 2015-09-16, 13:39

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?

wildrabbitt · 2015-09-16, 14:36

If you'll give me a couple of days max to prove my lemma I'll learn to TEX.

Deal?

wildrabbitt · 2015-09-16, 14:42

Actually I think I do have it. Hang on.

axn · 2015-09-16, 15:47

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.

wildrabbitt · 2015-09-16, 20:03

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

wildrabbitt · 2015-09-16, 20:09

This might help to visualise the issue :

http://www.mersenneforum.org/attachm...1&d=1442434165

wildrabbitt · 2015-09-16, 20:17

Pages 3 and 4 :

http://www.mersenneforum.org/attachm...1&d=1442434602

http://www.mersenneforum.org/attachm...1&d=1442434602

VBCurtis · 2015-09-16, 20:41

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!

LaurV · 2015-09-17, 01:55

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

wildrabbitt · 2015-09-17, 17:13

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

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, 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	Pages 3 and 4 : http://www.mersenneforum.org/attachm...1&d=1442434602 http://www.mersenneforum.org/attachm...1&d=1442434602 Attached Thumbnails

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

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, 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.

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