[FOM] Irrational numbers

[Dean Buckner]

Imagine we are given ALL the irrational numbers EXCEPT pi.  How exactly
would this fact manifest itself?  And what would change if pi were added?

If I search hard enough, I can find some rational number whose expansion
appears to correspond to that of pi.  Of course, for any such rational
series, there is a point which the expansion must diverge.  But then I can
find another one that agrees with the expansion of pi "still further".

So if we now add pi, what exactly changes?  At what point is pi "now really
needed"?  At EVERY point, it has a companion (in the set from which it was
omitted) agreeing with it from the beginning up to that point.  So how is pi
actually necessary?

Doesn't that prove that pi is not "the extension of an infinite decimal
fraction", that it's just a rule or algorithm of some sort?


["Set theory is wrong because it apparently presupposes a symbolism which
doesn't exist instead of one that does exist (is alone possible).  It builds
on a fictitious symbolism, therefore on nonsense."

"Mathematics is ridden through and through with the pernicious idioms of set
theory.  *One* example of this is the way people speak of the line as
composed of points.  A line is a law and isn't composed of anything at all".
(Wittgenstein, Remarks, XV § 173)


Dean Buckner
London
ENGLAND

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