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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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quasi

Posts: 12,062
Registered: 7/15/05
Re: Warning to visitors to sci.math
Posted: Mar 9, 2012 6:16 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Fri, 9 Mar 2012 20:42:53 +1100, "DavidW" <no@email.provided> wrote:

>> So let me ask you some questions ...
>>
>> (1) Did the OP present anything that would qualify as
>> a mathematical argument?

>
>Many times previously. But I'll pose a question: Is it
>possible to have a container in which you can find all
>natural numbers?


In theory, yes.

In the physical world, no.

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. It's the ability
to create conceptual objects that gives math its amazing
reach -- it's not tied down to physical realizability. The
only requirement for a mathematical theory is that it not
be provably inconsistent. In other words, if a theory
yields no logical contradiction (within an accepted
framework of logic), then it's legal.

As an example, consider Geometry.

In Geometry, a straight line goes on forever in both directions.

In the real world, there are no straight lines.

In Geometry, a point is an object with zero size.

In the real world, any object has positive volume.

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.

In the real world, a container with infinitely many objects is
impossible.

Thus, the human mind has the ability to create conceptual
objects which are not physically realizable, and then deduce
logically consistent results about the properties of such
objects.

quasi


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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Richard Tobin
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
3/8/12
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DavidW
3/8/12
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DavidW
3/8/12
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DavidW
3/8/12
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J. Antonio Perez M.
3/8/12
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DavidW
3/8/12
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J. Antonio Perez M.
3/9/12
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DavidW
3/9/12
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Brian Chandler
3/9/12
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DavidW
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DavidW
3/9/12
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DavidW
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Frederick Williams
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DavidW
3/9/12
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Frederick Williams
3/9/12
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DavidW
3/9/12
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J. Antonio Perez M.
3/10/12
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Frederick Williams
3/10/12
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DavidW
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DavidW
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Harrison Hill
3/12/12
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Tom P
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3/12/12
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J. Antonio Perez M.
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DavidW
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Horand.Gassmann@googlemail.com
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DavidW
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Lanarcam
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quasi
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quasi
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3/10/12
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3/12/12
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