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You are not logged in. #1 20060721 23:01:05
pi and other numbers with infinite numbers of decimalsi was just thinking about Pi's decimals. If they continue forever, every number should appear an infinite number of times. and if that is true, every number combination that exists, should also appear, and if it appear once it should appear an infinite numbers of times. so for example the number combination 4738002863772894374738387388399 appears an infinite number of times in Pi's decimals... Last edited by Kurre (20060722 03:32:24) #2 20060722 03:03:24
Re: pi and other numbers with infinite numbers of decimalsits possible, but not definate, because pi's digits aernt random, so theres no surety that the combination will be present in an infiniate given number of digits The Beginning Of All Things To End. The End Of All Things To Come. #3 20060722 03:28:11
Re: pi and other numbers with infinite numbers of decimalsThat's a tough question. I think you could have an irrational number that never had "666" in it. igloo myrtilles fourmis #4 20060722 03:38:27
Re: pi and other numbers with infinite numbers of decimals
no but they doesnt repeat and start over from 14159 (or at least noone has seen any kind of pattern in it as far as i know), so it must be an irrational order all the way...and since there are an infinite amount of numbers.....:p #5 20060722 04:25:08
Re: pi and other numbers with infinite numbers of decimals
infinate amount of numbers doesnt mean infinate amount of combinations, take for example The Beginning Of All Things To End. The End Of All Things To Come. #6 20060722 05:13:52
Re: pi and other numbers with infinite numbers of decimalsKurre, as luca pointed out, you make the assumption that pi's digits are random. That does have to be the case. "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 20060722 09:54:02
Re: pi and other numbers with infinite numbers of decimals9 could stop occuring? Then there would be a finite number of 9s. But how would you prove it? "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #8 20060722 19:04:37
Re: pi and other numbers with infinite numbers of decimals
But luca, that doesn't make any sense. If there was an infinite amount of 1's, then they wouldn't stop and suddenly end with a 2, because then the 1's must be finite. Bang postponed. Not big enough. Reboot. #9 20060723 01:13:25
Re: pi and other numbers with infinite numbers of decimals
This is an interesting thread. I'm inclined to believe the original poster's proposition. Making the assumption that pi really is an irrational number (lack of evidence of being rational is not proof that it's irrational), then there are an infinite number of decimal places. Even if the odds were 1 in 10^100 of a nine appearing, there would still be occurrences of nines occurring repetitively, as 1 in 10^100 are much better odds than 1 in infinity. You can shear a sheep many times but skin him only once. #10 20060723 01:19:48
Re: pi and other numbers with infinite numbers of decimalsInteresting question. IPBLE: Increasing Performance By Lowering Expectations. #11 20060723 01:20:44
Re: pi and other numbers with infinite numbers of decimals
If pi's digits aren't random, isn't that evidence that pi is in fact not irrational? If they are not random, that implies a pattern exists, even if we don't yet understand it. You can shear a sheep many times but skin him only once. #12 20060723 01:22:26
Re: pi and other numbers with infinite numbers of decimalsSuch numbers are called normal. IPBLE: Increasing Performance By Lowering Expectations. #13 20060723 02:31:38
Re: pi and other numbers with infinite numbers of decimals
To whom are you responding? You can shear a sheep many times but skin him only once. #14 20060723 02:37:43
Re: pi and other numbers with infinite numbers of decimalsI am of the belief that there are patterns of digits of long lengths that won't exist in pi. igloo myrtilles fourmis #15 20060723 03:34:35
Re: pi and other numbers with infinite numbers of decimalsI'm talking about the randomination of the numbers (for example pi). IPBLE: Increasing Performance By Lowering Expectations. #16 20060723 05:04:18
Re: pi and other numbers with infinite numbers of decimals
If time went on forever, there will always be time to do at least one more thing. If there is always time to do at least one more thing, there would be no reason to have to pick and choose since you would have time to do everything. You can shear a sheep many times but skin him only once. #17 20060723 05:14:55
Re: pi and other numbers with infinite numbers of decimalsWell, you're assuming pi doesn't have an exact value, but it does  as far as I've understood. It is EXACTLY: where P is the perimeter of a circle and d is its diameter. So just because we can't seem to find a pattern, it doesn't have to mean the digits are random. Or am I totally off track?#18 20060723 05:33:52
Re: pi and other numbers with infinite numbers of decimals
I don't think anyone is claiming Pi does not have an exact value. It is just an exact value that cannot be shown with a ratio of two integers. You can shear a sheep many times but skin him only once. #19 20060723 06:45:00
Re: pi and other numbers with infinite numbers of decimals"Random" has a meaning implied behind it which I think many have not heard of. "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..." #20 20060723 07:08:50
Re: pi and other numbers with infinite numbers of decimals
I think the important thing to remember is that since Pi has an infinite number of decimal places without a recognizable pattern, it does not matter if 1 appears more often than 5, since they will both appear an infinite number of times. The same goes for 09821346598712985170279561278934560 and 98435019823450928834087 both of which should appear an infinite number of times. Pi has been calculated to millions of decimal places, but that is still just a drop in the bucket of the infinite number of decimal places the irrational number contains. You can shear a sheep many times but skin him only once. #21 20060723 11:00:02
Re: pi and other numbers with infinite numbers of decimalsBut, just because the pattern is unrecognizable, we can't be sure that every number will appear only finite number of times. IPBLE: Increasing Performance By Lowering Expectations. 