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Topic: Warning to visitors to sci.math
Replies: 266   Last Post: Mar 19, 2012 9:13 AM

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Michael Stemper

Posts: 671
Registered: 6/26/08
Re: Warning to visitors to sci.math
Posted: Mar 9, 2012 1:31 PM
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In article <jjdfcc$r3v$1@speranza.aioe.org>, "DavidW" <no@email.provided> writes:
>quasi wrote:
>> On Fri, 9 Mar 2012 20:42:53 +1100, "DavidW" <no@email.provided> wrote:

>> But natural numbers are not elements of the physical world.
>> They are conceptual entities, as are sets of such numbers.
>> Mathematics allows for the conceptualization of objects
>> such as the set of all natural numbers.

>
>But it's an impossible concept. There can be no such thing as "all" if there
>are infinitely many.


I contend that there is such a thing as the set of all natural numbers.
I refer to this set as "N".

Since you contend that there is no such thing as an infinite set, there
are obviously natural numbers that are not in "N". Please name three
of them.

> You might be able to, for example, write a simple
>iterative formula to define the set, but you can never complete the iterations.


You don't have to "complete the iterations" in order to reason about
the elements of the set. For instance, I can work out that all elements
of the set of even numbers are divisible by two, without writing down
all of them -- or any of them.

> There's no
>such thing as all of them to contain.


If there's not "all" of them, there must only be "some" of them. Who
decides which ones there are and which ones there aren't?

>> In Geometry, we can have 2 points as close to each other as
>> we please.
>>
>> In the real world, distinct objects can get close but not
>> arbitrarily close.
>>
>> In Geometry, we regard a line as containing infinitely many
>> points.

>
>I have no problem with any of these. All they require is imagination to
>conceive. But the very concept of containing "all" of something of which there
>are infinitely many is self-contradictory.


Does your imagination allow a line segment to include all of its points?

--
Michael F. Stemper
#include <Standard_Disclaimer>
If this is our corporate opinion, you will be billed for it.


Date Subject Author
3/7/12
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DavidW
3/7/12
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adamk
3/8/12
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Brian Chandler
3/8/12
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Shmuel (Seymour J.) Metz
3/8/12
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amzoti
3/9/12
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micky
3/8/12
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Frederick Williams
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DavidW
3/8/12
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DavidW
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DavidW
3/8/12
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J. Antonio Perez M.
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DavidW
3/8/12
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DavidW
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J. Antonio Perez M.
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Horand.Gassmann@googlemail.com
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J. Antonio Perez M.
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Daryl McCullough
3/17/12
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Michael Stemper
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3/10/12
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