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Topic: Weierstrass
Replies: 26   Last Post: Jul 9, 2004 4:27 PM

 Messages: [ Previous | Next ]
 Dave Seaman Posts: 3,624 Registered: 12/8/04
Re: Weierstrass
Posted: Jul 9, 2004 10:36 AM

On Fri, 09 Jul 2004 15:10:09 +0100, Eckard Blumschein wrote:
> Jesse F. Hughes wrote:

>>>Isn't the mathematical meaning: Zero is included as well as
>>>excluded?

No.

> I do not doubt that David W. Cantrell is correct when he tells me that
> the empty set does not include zero if it includes nothing. I just
> wonder how to decide whether it is open or closed if zero is not
> included and not excluded.

The definitions of open and closed does not mention the presence or
absence of zero at all; it's completely irrelevant.

>> Included and excluded in what? How would that be the meaning?

> As a layman, I associate open or closed sets and intervals with excluded
> or included front-numbers, respectively. In N, [4, 7) means 4, 5, 6
> while (4, 7] means 5, 6, 7. Is this correct?

That notation is generally used to indicate intervals on the real line.
If you interpret them as subsets of N, then your conclusions are correct,
but each of those sets that you mentioned is both open and closed in N
with the standard metric. As subsets of R, neither set is open and
neither is closed.

--
Dave Seaman
Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling.

Date Subject Author
7/8/04 Eckard Blumschein
7/8/04 Herman Jurjus
7/9/04 Eckard Blumschein
7/9/04 Robin Chapman
7/9/04 Eckard Blumschein
7/9/04 Jesse F. Hughes
7/9/04 David W. Cantrell
7/9/04 Eckard Blumschein
7/9/04 David W. Cantrell
7/9/04 Jesse F. Hughes
7/9/04 Eckard Blumschein
7/9/04 Dave Seaman
7/9/04 Jesse F. Hughes
7/9/04 Virgil
7/9/04 David C. Ullrich
7/9/04 Virgil
7/9/04 David C. Ullrich
7/9/04 Thomas Mautsch
7/9/04 Robin Chapman
7/9/04 Virgil
7/9/04 Virgil
7/9/04 Virgil
7/9/04 Eckard Blumschein
7/9/04 Virgil
7/9/04 Virgil
7/8/04 Virgil
7/8/04 Robin Chapman