On 24 Sep 2011, at 20:56, 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. All of it's definitions require
infinities. If these infinities don't exist, because your
philosophy of mathematics is constructivist, then it follows that Pi
does not exist.
Actually, finitists, constructivists and intuitionists have not so
much problem with Pi, nor Euler's e and gamma, as those numbers are
computable real numbers, and admit clean finite definition, and
methods for handling them unambiguously. They have problem with the
non constructive notion of arbitrary real number, or with non
computable number. But then they have problem with any non solipistic
account of reality. Brouwer, the founder of intuitionism would have
said to his student that his philosophy makes them non existing, and
that he was astonished they were interested in it (I don't know if
this is a legend, or relate to something true).
This short remark makes not your point non valid, to be sure.
Bruno
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.
Jason
Brent
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