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| William Elliot |
 Posted: Fri Apr 25, 2008 3:14 am |
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Riddle of the day.
Do you have to be a member to get into a set? |
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| LauLuna |
| Posted: Sat Apr 26, 2008 5:14 am |
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On Apr 25, 10:14 am, William Elliot <ma...@hevanet.remove.com> wrote:
Quote: Riddle of the day.
Do you have to be a member to get into a set?
It depends on how elitist the set is.
The most elitist set -the empty set- does not impose such condition. |
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| John Jones |
| Posted: Sat Apr 26, 2008 12:48 pm |
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Joined: 26 Oct 2004
Posts: 4263
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LauLuna wrote:
Quote: On Apr 25, 10:14 am, William Elliot <ma...@hevanet.remove.com> wrote:
Riddle of the day.
Do you have to be a member to get into a set?
It depends on how elitist the set is.
The most elitist set -the empty set- does not impose such condition.
Isn't '"the" empty set' a misapplication of a definite article? |
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| Jan Burse |
| Posted: Sat Apr 26, 2008 5:43 pm |
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J Jones schrieb:
Quote: LauLuna wrote:
On Apr 25, 10:14 am, William Elliot <ma...@hevanet.remove.com> wrote:
Riddle of the day.
Do you have to be a member to get into a set?
It depends on how elitist the set is.
The most elitist set -the empty set- does not impose such condition.
Isn't '"the" empty set' a misapplication of a definite article?
No, for example in ZFC, by the axiom of extensionality, the
empty sets are all equal. And therefore there is only one
empty set, and we can refer to it as "the" empty set. |
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| Butch Malahide |
| Posted: Sun Apr 27, 2008 7:39 am |
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On Apr 27, 10:13 am, Jan Burse <janbu...@fastmail.fm> wrote:
Quote:
So thats why the arabs are smarter than the americans. They invented
the zero, to assess that for example there are zero ears of rice
in their store.
Really? I thought the Hindus invented zero. |
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| John Jones |
| Posted: Sun Apr 27, 2008 9:41 am |
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Joined: 26 Oct 2004
Posts: 4263
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Jan Burse wrote:
Quote: J Jones schrieb:
LauLuna wrote:
On Apr 25, 10:14 am, William Elliot <ma...@hevanet.remove.com> wrote:
Riddle of the day.
Do you have to be a member to get into a set?
It depends on how elitist the set is.
The most elitist set -the empty set- does not impose such condition.
Isn't '"the" empty set' a misapplication of a definite article?
No, for example in ZFC, by the axiom of extensionality, the
empty sets are all equal. And therefore there is only one
empty set, and we can refer to it as "the" empty set.
I can't think what 'equality' could mean if that equality has been
assessed on the grounds that there is nothing by which equality can be
assessed. |
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| Jan Burse |
| Posted: Sun Apr 27, 2008 10:13 am |
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J Jones schrieb:
Quote:
I can't think what 'equality' could mean if that equality has been
assessed on the grounds that there is nothing by which equality can be
assessed.
So thats why the arabs are smarter than the americans. They invented
the zero, to assess that for example there are zero ears of rice
in their store.
The empty set assesses that it has no elements. And a consequence
of this assessment, because of the axiom of extenionality, is the
asssessment that empty sets are unique. There is only one empty
set on the object level.
But if you want you can give them multiple names on the meta
level, such as:
anna = {}
bert = {}
Although the names are different, the two sets are equal.
Although the two sets are equal, the names are different.
Take any decent book about first order logic plus any decent
book about set theory.
Bye |
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| John Jones |
| Posted: Sun Apr 27, 2008 5:36 pm |
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Joined: 26 Oct 2004
Posts: 4263
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Jan Burse wrote:
Quote: J Jones schrieb:
I can't think what 'equality' could mean if that equality has been
assessed on the grounds that there is nothing by which equality can be
assessed.
So thats why the arabs are smarter than the americans. They invented
the zero, to assess that for example there are zero ears of rice
in their store.
The empty set assesses that it has no elements. And a consequence
of this assessment, because of the axiom of extenionality, is the
asssessment that empty sets are unique. There is only one empty
set on the object level.
But if you want you can give them multiple names on the meta
level, such as:
anna = {}
bert = {}
Although the names are different, the two sets are equal.
Although the two sets are equal, the names are different.
Take any decent book about first order logic plus any decent
book about set theory.
Bye
will respind in a general post, but don't you feel that something is
wrong with the idea of an empty set? |
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| Jesse F. Hughes |
| Posted: Mon Apr 28, 2008 8:57 am |
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Jan Burse <janburse@fastmail.fm> writes:
Quote: J Jones schrieb:
I can't think what 'equality' could mean if that equality has been
assessed on the grounds that there is nothing by which equality can be
assessed.
So thats why the arabs are smarter than the americans. They invented
the zero, to assess that for example there are zero ears of rice
in their store.
The brilliant John Jones is at the University of Cardiff. I'm afraid
we lowly Americans can't claim Jones as one of our philosophical
pillars.
--
"Basically I see myself as a hero in a great drama, and that is part of
how I motivate myself through failures and a lot of negativity, like
from people like you. So the Hammer is part of my own personal story,
my personal myth." -- James S. Harris, a legend in his own mind |
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