Define a function,

as,

Prove that there for any there exists an such as,

Tried to prove it, seems extremely complicated.

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- May 9th 2006, 07:06 PMThePerfectHackerHelp me with problem.
Define a function,

as,

Prove that there for any there exists an such as,

Tried to prove it, seems extremely complicated. - May 9th 2006, 09:15 PMCaptainBlackQuote:

Originally Posted by**ThePerfectHacker**

A number for which such a exists is called Wondrous Number.

The conjecture that all numbers are Wondrous is I believe still open.

RonL - May 10th 2006, 05:22 AMc_323_h
what does mean? are there any books where I can learn about proofs, but are at a high school level? I can write a simple computer program to determine if a number is wondrous or not (at least is sounds simple). I will post the code sometime, when i have a chance to write the program.

- May 10th 2006, 05:43 AMCaptainBlackQuote:

Originally Posted by**c_323_h**

(from Zahlen - German for number?).

denotes the set of all positive integers , (also )

Quote:

Are there any books where I can learn about proofs, but are at a high school level?

"Mathematics: A Very Short Introduction"

Tim Gowers

ISBN-10: 0-19-285361-9

Quote:

I can write a simple computer program to determine if a number is wondrous or not (at least is sounds simple). I will post the code sometime, when i have a chance to write the program.

ever terminate.

RonL - May 10th 2006, 07:00 AMc_323_hQuote:

Originally Posted by**CaptainBlack**

- May 10th 2006, 08:16 AMCaptainBlackQuote:

Originally Posted by**c_323_h**

of of the Web. Google should yurn up a number of them.

RonL - May 10th 2006, 08:51 AMCaptainBlackQuote:

Originally Posted by**ThePerfectHacker**

It might be interesting to define an -wondrous numberto be

one for which the itteration teminates in exactly -steps.

The you could ask what proportion of numbers less

than of equal to are -wondrous.

RonL - May 10th 2006, 02:25 PMThePerfectHackerQuote:

Originally Posted by**CaptainBlack**

- May 10th 2006, 07:09 PMThePerfectHackerQuote:

Originally Posted by**CaptainBlack**

- May 12th 2006, 09:36 PMCaptainBlackQuote:

Originally Posted by**ThePerfectHacker**

numbers.

Consider , this is obviously -wondrous.

So there is at least one Wondrous number for every .

Hence there are an infinite number of Wondrous numbers.

RonL - May 12th 2006, 10:49 PMrgep
Before you spend a lot of time on this famous problem, you should probably look at some of the resources listed in the ODP.

- May 13th 2006, 08:27 AMSkyWatcherQuote:

Originally Posted by**ThePerfectHacker**

- May 13th 2006, 08:38 AMCaptainBlackQuote:

Originally Posted by**SkyWatcher**

proof of Collatz's, conjecture is wrong? (this is the first link on the page given

in rgep's post - I must say that on a cursory examination it looks wrong)

RonL - May 14th 2006, 07:06 PMThePerfectHackerQuote:

Originally Posted by**SkyWatcher**

For anybody else, who does not understand the joke it is private. I once answered a lot of questions all of which where solved with continued fractions. SkyWatcher was obsessed with them ever since. Now he made that remark as if to tease me to solve this problem with continued fractions too. - May 14th 2006, 07:08 PMThePerfectHackerQuote:

Originally Posted by**CaptainBlack**