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Science Forum Index » Logic Forum » The axiom of extensionality and the Empty Set
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| John Jones |
 Posted: Sun Apr 27, 2008 5:47 pm |
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Joined: 26 Oct 2004
Posts: 4263
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Three problems:
If I say 'bring me a set of cutlery' and the last set of cutlery has
already been taken, does that make the set 'empty' because of the axiom
of extensionality?
If I say 'bring me the set of no objects' would the fact that you cannot
bring me any such set mean that there IS such a set and that by the
axiom of extensionality 'it' is 'empty'?
Would the axiom of extensionality ensure that the set 'the set of
unforsen movments' must gradually lose its letters until it becomes
'empty', i.e. until it becomes 'the set ' ? |
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| george |
| Posted: Sun Apr 27, 2008 5:47 pm |
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On Apr 27, 6:47 pm, J Jones <jonescard...@aol.com> wrote:
Quote: Three problems:
These are REALLY stupid questions.
Quote: If I say 'bring me a set of cutlery'
Then NO MATHEMATICIAN WILL GIVE A SHIT
because cutlery is concrete and math is abstract. |
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| Jan Burse |
| Posted: Sun Apr 27, 2008 7:31 pm |
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J Jones schrieb:
Quote: Three problems:
If I say 'bring me a set of cutlery' and the last set of cutlery has
already been taken, does that make the set 'empty' because of the axiom
of extensionality?
It seems you dont know the axion extensionality, isn't it?
Quote: If I say 'bring me the set of no objects' would the fact that you cannot
bring me any such set mean that there IS such a set and that by the
axiom of extensionality 'it' is 'empty'?
Seems you dont know the definition of empty set, isn't it?
Quote: Would the axiom of extensionality ensure that the set 'the set of
unforsen movments' must gradually lose its letters until it becomes
'empty', i.e. until it becomes 'the set ' ?
Cantor defined what a mathematical set should be. The element hood
must be determined or some such.
So common "set"s are not necessarely mathematical "set"s.
Bye |
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| Jan Burse |
| Posted: Sun Apr 27, 2008 7:41 pm |
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Jan Burse schrieb:
Quote: Cantor defined what a mathematical set should be. The element hood
must be determined or some such.
So common "set"s are not necessarely mathematical "set"s.
By a "set" we understand every collection to a whole of
**definite**, well differentiated objects of our intuition
or our thought.
Cantor, 1895, p. 282 |
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| John Jones |
| Posted: Mon Apr 28, 2008 6:22 am |
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Joined: 26 Oct 2004
Posts: 4263
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george wrote:
Quote: On Apr 27, 6:47 pm, J Jones <jonescard...@aol.com> wrote:
Three problems:
These are REALLY stupid questions.
If I say 'bring me a set of cutlery'
Then NO MATHEMATICIAN WILL GIVE A SHIT
because cutlery is concrete and math is abstract.
Crikey, that's a stupid response 'george'. I have to say it again
because once isn't enough. It's a really stupid response. |
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| John Jones |
| Posted: Mon Apr 28, 2008 6:29 am |
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Joined: 26 Oct 2004
Posts: 4263
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Jan Burse wrote:
Quote: Jan Burse schrieb:
Cantor defined what a mathematical set should be. The element hood
must be determined or some such.
So common "set"s are not necessarely mathematical "set"s.
By a "set" we understand every collection to a whole of
**definite**, well differentiated objects of our intuition
or our thought.
Cantor, 1895, p. 282
Thankyou. You are such a dear.
Cantor's definition of set is obviously not the same as ZFC's idea of a
set because Cantor, like me, said that a set must be a whole. Like for
example a bouquet. The difference between Cantor and me is that Cantor
thought that the objects in a set must be definite, while I say that the
whole must ALSO be definite.
But if Cantor's definition is right, and that a set must contain
definite objects, then how can there be an empty set? An empty set must
be an invention of ZFC, an invention which has nothing to do with
Cantor's set at all. |
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| Jan Burse |
| Posted: Mon Apr 28, 2008 11:19 am |
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J Jones schrieb:
Quote: An empty set must be an invention of ZFC, an invention which
has nothing to do with Cantor's set at all.
Look further into Cantors 1883 work(*).
Somewhere he writes:
R is so constituted that by repetion of the
derivation process it can be reducated to
annihilation, so that there is always
a first number g of the number classes
(I) or (II) for which
R^g = 0
such point-sets I call reducible.
So better take ZFC as a clearn up of Cantor, than
something alien to Cantor.
Best Regards |
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