See page 400 of "Gödel Escher Bach" by Douglas Hofstadter.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.
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.
denotes the set of all integers ,Originally Posted by c_323_h
(from Zahlen - German for number?).
denotes the set of all positive integers , (also )
I quite like (meaning I like it a lot):Are there any books where I can learn about proofs, but are at a high school level?
"Mathematics: A Very Short Introduction"
You will have no guarantee that for any particular number that it willI 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.
yeah, i intend i using a loop and it could iterate forever (theoretically). but the largest number my programs can go up to is 2 billion, which is disappointing. as soon as it reaches this number it terminates (i code using c++). i may have to write a new class with arrays to hold more digits, but even with this there is no guaranteeOriginally Posted by CaptainBlack
Let's assume you are asking for a proof to the infinitude of WondrousOriginally Posted by ThePerfectHacker
Consider , this is obviously -wondrous.
So there is at least one Wondrous number for every .
Hence there are an infinite number of Wondrous numbers.
I have got an elegant solution to your problem, it use discontinued fraction (a variety of continued fraction) and takes only eleven pages. I hope i have not made a mistake because apparently your not very qwick to find mistakes on this site even when they are elementary!Originally Posted by ThePerfectHacker
Do you have a demonstration that Feinstein's proof that there can be noOriginally 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)
Ha ha ha,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.