Re: Exact-Point paradox

On Jul 9, 1:58 pm, Said Alyami <said_...@xxxxxxxxx> wrote:


5) There cannot be a very next point to X1 on the real numbers line,
so the point X2 does not exist, and because X2 does not exist then X3
does not exist too, hence X4 does not exist, hence X5, X6, X7, X8,...
to INFINTIY do not exist.

6) From (6), we can see that the non-existence of the "very next
point" goes to infinity, like what happens in Domino tiles after the
fall of the very first one, then the effect of falling continue
through all the next other tiles.

7) From (6) , we can see that there will be no points at all after
the exact point X1 which represents the real number 1.

No real has an immediate successor under the < order, that's true; the
immediate successor of 1, and the immediate successor of the immediate
successor of 1, etc. don't exist; but it does not follow that there is
no real after 1. When you discard X2, X3, ... you are discarding non
existent numbers, so whatever existed, continues to exist.

I'd say you are still trying to understand the continuum as a discrete
order.

6) There exists a positive real number Kz that is "less than or equal
to" any fraction that is represented by any 9 in 0.999...

I assume you mean there's is one positive real which is less than or
equal to any number in the sequence 0.9, 0.09, 0.009,... Well, no; it
doesn't exist; for each positive real r you can reach along the
sequence a term strictly less than r.

It's true that for any number in the sequence there is a positive real
less than or equal to it, but there is not ONE positive real less than
or equal to ALL of them.

So, your Kz does not exist.

Regards

.

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