Re: The infintely small number b

On Nov 23, 12:53 am, Marshall <marshall.spi...@xxxxxxxxx> wrote:
On Nov 22, 10:06 pm, Venkat Reddy <vred...@xxxxxxxxx> wrote:

To clarify further, "inclusive" bounds and "exclusive" bounds do not
makes sense for a finite interval in continuum.

Actually, I'

Ahem.

Actually, I've proven that they do make sense. You need to
respond to that proof. (Well, actually, you'll need to read it
and understand it first. Let me know if you have any questions.)


There are only one
kind of bounds - that which define the interval itself. Anny other
extra kind of bounds are superfluous or redundant.

Again: I've proven this false.


For you to understand all this, as I've told before on these threads,
you need to thiink of continuum just as it is, not a set or collection
of single kind of things.

"Just as it is" is exactly and precisely what we can prove
about it. Since I've proven, without reference to any
theory of sets or collections, using only simple properties
of the real numbers, that your claim that bounds are necessarily
inclusive is false, "just as it is" means that some bounds
are exclusive.

You've said that you're only interested in using high school
math. So, using only high school math, I showed how your
claims do not apply to the real numbers. Please, using only
high school math, respond to the proof. Complete failure
to respond suggests either an inability to comprehend or
a recognition that the proof destroys your argument.


Marshall
.

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