On 9/24/2011 11:56 AM, Jason Resch wrote:
On Sep 24, 2011, at 12:44 PM, meekerdb <meeke...@verizon.net> wrote:
On 9/24/2011 12:07 AM, Jason Resch wrote:
A final consideration: do you believe Pi has such a value that when Euler's number is
raised to the power of (2*Pi*i) the result is 1? Pi has a value which no human has
determined, as determinig it requires infinite time and memory. If only those
mathematical things known to humans exist, then Pi's true value does not exist.
I think this is questionable. One can use the value of pi, calculate with it,
determine it's relation with other quantities.
We can use an approximation of it's value, or a definition of how to derive it's value
(given infinite time and memory), but we've never known or used it's value.
Sure we do: sin(pi/4) = 1/sqrt(2) uses the value. So does e^(i*pi) = -1.
All of it's definitions require infinities.
The circumference of a circle whose diameter is 1.
If these infinities don't exist, because your philosophy of mathematics is
constructivist, then it follows that Pi does not exist.
In one (of the many) senses of "exist".
So you can't write it's decimal expansion, how significant is that?
Sure everything is questionable. But according to Rogers theory the unnown digits of Pi
do not exist and/or have no definite value since no human has determined them.
What this equation and reasoning suggests is that there can be certain values which are
unknown to us. Such as the googolplexth digit of Pi.
I'd say almost all (in the measure theoretic sense) values are unknown to us.
"By habit, whenever a man sees a name, he is led to figure
himself a corresponding object."
--- Jeremy Bentham (1748-1832)
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