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2004-12-12, 17:25   #56
jinydu

Dec 2003
Hopefully Near M48

2·3·293 Posts

Quote:
 Originally Posted by shaxper But the value of pi doesn't change, just the determination (the outcome) of that value.
That's my point. The value of pi can never change, hence it cannot be random. Sure, the outcome of the computation can change, but that doesn't make it random. If I try to write 1/3 in decimal form, the outcome depends on the number of 3's I choose to write down, but it certainly doesn't mean that the value of 1/3 is random.

 2004-12-12, 19:43 #57 TTn   86016 Posts Guy's Law, means you cant make accurate predictions about such things, since it all lie beyond infinity... well 99.9999... % of it lay there. Our sentient nature, is merely an iota of what is the truth.
 2004-12-12, 20:38 #58 jinydu     Dec 2003 Hopefully Near M48 33368 Posts Of course we can make such predictions. For instance, I can prove with 100% certainty that every digit in the decimal expansion of 1/3 is 3. Although such precise predictions about the decimal expansion of pi cannot be made (at least not yet), this certainly doesn't mean that pi is random. If you think about it, a decimal expansion is a rather arbitrary way of representing a number. In the case of a real number between 1 and 10, the representation is: d0 + d1*10^-1 + d2*10^-2 + d3*10^-3 + d4*10^-4 + ... where d0, d1, d2, d3, d4 ... are integers from 0 to 9. But what is so special about this form of representation? Its just one way to express a (potentially infinite) series. The observation that the digits of pi are unpredictable just shows that a decimal expansion is not a very good way to represent pi. But this doesn't mean that all representations will be unsuccessful. In fact, some other infinite series representations are not only successful, but stunningly beautiful. Once again, I cite the equation: 1 + 1/4 + 1/9 + 1/16 + 1/25 + 1/36 + ... = (pi^2)/6
2004-12-13, 00:22   #59
TTn

23×3×233 Posts

Ofcourse 1/3 has all three's in it's expansion.
Iff, you are moving foward in time, that sounds fair.

Quote:
 Once again, I cite the equation: 1 + 1/4 + 1/9 + 1/16 + 1/25 + 1/36 + ... = (pi^2)/6
Very nice, but i prefer the product of primes divided by the product of numbers one less than, or one more than a prime number.
Since the theorem should be "divergent", who is to say what order exists beyond our boundries?
Quote:
 2/1 * 3/2 * 5/6 * 7/6 * 11/10 * 13/14 * 17/18 * 19/18 * 23/22 * ...

Last fiddled with by TTn on 2004-12-13 at 00:23

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