Re: Question

In article <1146165177.094108.274750@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
zuhair <zaljohar@xxxxxxxxx> wrote:

Arturo Magidin wrote:

[.snip.]


I know that converges into zero is something else other than equal
zero.

Yet you asked for the index at which a sequence that converged to zero
had the terms equal to zero.

The definition states that if the difference converges into zero then
the two Cauchy sequences are equivalent, I disagree with that.

You cannot disagree with a definition. You can say that the definition
does not capture an idea that you have, or does not represent what you
think it should represent, but you cannot "disagree with a definition."


They should be equivalent only when the difference REACHES zero.

That would be something else, and not the definition of equivalence
which is used to define real numbers. Change the definition if you
want, but then you are not working with what every one else in the
world calls the real numbers.

In other words: you are objecting to all of mathematics. You can play
with your own rules if you want, but be aware that what you are doing
has NOTHING to do with real numbers as they are understood by everyone
else in the world.

and it should specify at which number of terms that would happen.

Then your definition of "real numbers" does not agree with the
definition of anybody else. You can call them "zuhair numbers" if you
want, but then you need to PROVE everything about them, since nobody
else works with them.

Good luck, and keep me out of it.


So I am questioning the definition itself.

What you are doing is saying that you don't like the
definition. That's YOUR problem, not the problem of the definition. It
means you are unwilling to work with the standard rules as they relate
to real numbers. You can do that, but then you are NOT working with
real numbers.

That was my question, can you answer it.

The answer is: you are not working with real numbers. You are working
with an invention of yours that are not what everyone else in the
world calls the real numbers. Calling them "real numbers" is either
confused or dishonest on your part.

Everything you have said is nonsense if we use the words "ordinal",
"cardinal", "natural", "omega", "real number", "decimal expansion",
etc. in their STANDARD usages.

Since you seem only interested in playing with yourself, do go ahead.


--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes")
======================================================================

Arturo Magidin
magidin@xxxxxxxxxxxxxxxxx

.

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