On 7/17/2011 11:50 AM, Jason Resch wrote:
For Euler's identity to hold, Pi must exist in its infinitely precise form, but Pi does not exist in its infinitely precise form anywhere in this universe.
You don't know that, since space may well be a continuum (c.f. the recent paper by Feeney et al).
Ben believes mathematical truth only exists in our minds, but does Pi really exist in our minds, or only the notion that it can be derived as the ratio between a plane circle and its diameter?
But that's the characteristic of mathematics, its statements are notions and notions are things in minds. So there is no difference between the notion of pi existing in our minds and pi "really" existing in our minds.
Pi is so big that its digits contain all movies and all books ever created, surely this is not present within our minds,
Expressing pi as a sequence of digits is a notion in our minds. The sequence is no more in our minds than is 10^10^100.
but it is exactly what must exist for e^(2*Pi*i) = 1.
I disagree. For Euler's identity to hold just means that if follows logically from some axioms we entertain.
Brent
Jason
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