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#1 2009-06-28 03:06:00

soroban
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Yet Another Number Trap

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#2 2009-06-28 04:01:06

mathsyperson
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Re: Yet Another Number Trap

[Jane had an attempted proof above this post]

Isn't the existence of other cycles a fairly famous open problem?
I'd be interested to see this proof you mention, soroban.

Jane, I'm not sure what you're doing. I can't see any mistakes in what you've written, but I also can't see you concluding anything. Sorry if I'm being dense. smile


Why did the vector cross the road?
It wanted to be normal.
 

#3 2009-06-28 05:01:05

bossk171
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Re: Yet Another Number Trap

I was under the impression that this was unsolved:

http://en.wikipedia.org/wiki/Collatz_conjecture


There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction.
 

#4 2009-06-28 06:55:49

bobbym
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Re: Yet Another Number Trap

Last result I know for it is (Oliveira e Silva 2008)

proved by computer for all numbers <= 5.47637715 10^18

Last edited by bobbym (2009-06-28 06:56:33)


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#5 2009-06-28 10:17:32

Ricky
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Re: Yet Another Number Trap

If M is odd, then we repeat from step one.

Let {x_n} be the sequence generated from your starting odd number.  So x_1 = 3*x_0 + 1 and x_2 = (3*x_0 + 1)/2.  Now in the case that x_2 is odd, we then have x_3 = (9*x_0 + 3)/2.  But the thing here is that x_3 > x_0.  If your M always turns out to be odd, then the sequence diverges to infinity.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."
 

#6 2009-06-28 10:20:37

Ricky
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Re: Yet Another Number Trap

JaneFairfax wrote:

Actually, Ive only proved that any number you start with will eventually be reduced to one that is congruent to 1 mod 3. I havent proved that it will eventually become 1. neutral

But there is an upside to this: I feel confident in awarding you the longest proof ever of that fact for this problem.

3n+1 = 1 (mod 3)

wink


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."
 

#7 2009-06-28 11:28:31

Ricky
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Re: Yet Another Number Trap

JaneFairfax wrote:

I was referring to an ODD number ≡ 1 mod 3! mad

Jane, please don't delete your posts after they have been replied to.  It makes other people who are trying to follow this thread rather confused.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."
 

#8 2009-06-28 20:22:59

JaneFairfax
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Re: Yet Another Number Trap

Then please stop making pointless replies to my posts. I had already admitted that my hastily thought-up proof was neither here nor there, so there was no point at all in commenting on it. neutral

Last edited by JaneFairfax (2009-06-28 20:56:27)


Q: Who wrote the novels Mrs Dalloway and To the Lighthouse?

A: Click here for answer.
 

#9 2009-06-29 01:40:32

Ricky
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Re: Yet Another Number Trap

Jane, mathsyperson posted:

Jane, I'm not sure what you're doing. I can't see any mistakes in what you've written, but I also can't see you concluding anything. Sorry if I'm being dense.

I was explaining to him what was wrong.  Don't be so embarrassed at making little mistakes.  I used the quadratic equation wrong in my algebra final not more than 2 months ago.  It happens.

At times you can learn more from mistakes.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."
 

#10 2009-06-29 02:44:59

bobbym
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Re: Yet Another Number Trap

Such a mature and caring answer. Someone has a lot friends on this forum, hope that person comes to realize that.

Awful to hear about that error on a final. Everyone can relate. Only good that can come from it is you probably won't ever forget it.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#11 2009-06-29 03:16:39

JaneFairfax
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Re: Yet Another Number Trap

Okay, thanks, Ricky. smile You are nice. kiss You do not insult me for making a typo, unlike integer. mad

What is wrong with integer anyway? When I made a careless typo  in another thread, he or she had to insult me by posting BS about my breakfast. There was absolutely no need for that! swear

Last edited by JaneFairfax (2009-07-26 23:07:19)


Q: Who wrote the novels Mrs Dalloway and To the Lighthouse?

A: Click here for answer.
 

#12 2009-07-20 12:02:08

quittyqat
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Re: Yet Another Number Trap

On most forums, what you just posted would not be allowed.


I'll be here at least once every month. XP
 

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