Re: Definition of real number ℝ --infinitesimal--

olcott <polcott2@gmail.com> writes:

On 3/29/2024 7:25 PM, Keith Thompson wrote:

[...]

What he either doesn't understand, or pretends not to understand, is
that the notation "0.999..." does not refer either to any element of
that sequence or to the entire sequence.  It refers to the *limit* of
the sequence.  The limit of the sequence happens not to be an element of
the sequence, and it's exactly equal to 1.0.
 

In other words when one gets to the end of a never ending sequence
(a contradiction) thenn (then and only then) they reach 1.0.

No.

You either don't understand, or are pretending not to understand, what
the limit of sequence is.  I'm not offering to explain it to you.

This is all stated in terms of the real numbers, which are a well
defined set.  There are other systems with different properties.  If we
were talking about the hyperreals, for example, olcott's statement might
be correct (though I'm not sure of that).  But olcott seems to be
insisting, quite incorrectly, that his statements apply to the reals.

>
Pi exists at a single geometric point on the number line.

Irrelevant.

[...]

--
Keith Thompson (The_Other_Keith) Keith.S.Thompson+u@gmail.com
Working, but not speaking, for Medtronic
void Void(void) { Void(); } /* The recursive call of the void */