Date: Oct 4, 2017 2:16 PM
Subject: Re: Zelos Malum can't even get the simplest logic correct.
When k is not a rational number, the convention
is of course that the interval (-oo, k) is viewed
as an interval of the real line,
and not an interval of the rational numbers. So
when you write (-oo, pi), for example e is also
part of this interval, since e < pi:
pi = 3.141592653589...
e = 2.718281828459...
But if you want to construct the reals from Q,
the rational numbers, then you don't have pi,
and you don't have intervals of the real line,
only subsets of the rational numbers Q. Do
you by any chance understand what it means to
construct the real numbers?
Am Mittwoch, 4. Oktober 2017 19:29:24 UTC+2 schrieb John Gabriel:
> Any cut of the form
> (m, k) U (k, n) where m < k and k < n
> is EQUIVALENT to
> (-oo, k) U (k, oo) where k is not a rational number.
> The tail parts (-oo,m) and (n, oo) which are discarded, are irrelevant. In fact, the tail parts do not feature in my disproof of the D. Cut and can be added in at any time without any loss of generality.