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On 02/04/2024 02:27, Keith Thompson wrote:olcott <polcott333@gmail.com> writes:>On 4/1/2024 6:11 PM, Keith Thompson wrote:"IDK, probably not."olcott <polcott333@gmail.com> writes:>
[...]Since PI is represented by a single geometric point on the number line[...]
then 0.999... would be correctly represented by the geometric point
immediately to the left of 1.0 on the number line or the RHS of this
interval [0,0, 1.0). If there is no Real number at that point then
there is no Real number that exactly represents 0.999...
In the following I'm talking about real numbers, and only real
numbers -- not hyperreals, or surreals, or any other extension to the
real numbers.
You assert that there is a geometric point immediately to the left
of
1.0 on the number line. (I disagree, but let's go with it for now.)
Am I correct in assuming that this means that that point corresponds
to
a real number that is distinct from, and less than, 1.0?
IDK, probably not. I am saying that 0.999... exactly equals this number.
Did you even consider taking some time to *think* about this?
PO just says things he thinks are true based on his first intuitions
when he encountered a topic. He does not "reason" his way to a new
carefully thought out theory or even to a single coherent idea. Don't
imagine he is thinking of hyperreals or anything - he just "knows"
that obviously any number which starts 0.??? is less than one starting
1.??? - because 0 is less than 1 !! Or whatever, it really doesn't
matter.
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