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Topic: Another AC anomaly?
Replies: 280   Last Post: Dec 27, 2009 3:53 PM

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mueckenh@rz.fh-augsburg.de

Posts: 18,076
Registered: 1/29/05
Re: Another AC anomaly?
Posted: Dec 8, 2009 4:31 PM
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On 8 Dez., 19:36, A <anonymous.rubbert...@yahoo.com> wrote:

>
> A function f is said to be continuous at a point x in its domain if
> the limit of f(a), as a approaches x, is equal to f(x); in others
> words, the limit of the values of f is equal to the value of f at the
> limit, speaking loosely. Of course, not every function is continuous
> at every point in its domain, and some functions are not even
> continuous at any point in their domains at all.
>
> The situation for sets and cardinality is no more mysterious than
> that. The cardinality of a limit of subsets of the integers is not
> guaranteed to be the limit of the cardinalities of those subsets. You
> don't expect an arbitrary function to always be continuous, so perhaps
> it's unreasonable to expect the cardinality "function," defined on
> subsets of the integers, to be continuous.-


That depends on the circumstances. If infinite sets exist, then they
have a cardinality.
Then the limit cardinality is the cardinality of the limit set.

If they do not exist but are merely an arbitrary, perhaps inconsistent
delusion, then everything is possible. I argue, based on Cantor's
claim, that infinite sets exist (in order to show that they do not).

Regards, WM


Date Subject Author
11/23/09
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of Bentley College
Marshall
12/2/09
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of Bentley College
Marshall
11/27/09
Read Re: Another AC anomaly?
William Hughes
11/27/09
Read Re: Another AC anomaly?
William Hughes
11/26/09
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mueckenh@rz.fh-augsburg.de
11/28/09
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11/26/09
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11/28/09
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11/26/09
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mueckenh@rz.fh-augsburg.de
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11/28/09
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11/29/09
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11/29/09
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11/30/09
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12/5/09
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12/1/09
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11/27/09
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11/27/09
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anonymous.rubbertube@yahoo.com
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Read Re: Another AC anomaly?
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11/27/09
Read Re: Another AC anomaly?
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11/27/09
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mueckenh@rz.fh-augsburg.de
11/27/09
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11/27/09
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Read Re: Another AC anomaly?
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11/27/09
Read Re: Another AC anomaly?
Virgil

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