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number system with infinities
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bo198214
Jan 31, 2008, 8:30:12 AM1/31/08
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Is there a linearly ordered field extending the reals (hopefully not
exceeding the cardinality of the set of the reals), in which every
increasing sequence has a limit?
exceeding the cardinality of the set of the reals), in which every
increasing sequence has a limit?
I was thinking about hyperreals or Conway numbers but couldnt quickly
derive an answer. Hyperreals seem not have this property.
G. A. Edgar
Jan 31, 2008, 11:00:34 AM1/31/08
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In article <fnsih4$na3$1...@news.ks.uiuc.edu>, bo198214
<bo19...@googlemail.com> wrote:
<bo19...@googlemail.com> wrote:
> Is there a linearly ordered field extending the reals (hopefully not
> exceeding the cardinality of the set of the reals), in which every
> increasing sequence has a limit?
No. In any ordered field, the sequence N of natural numbers
is defined, and it has no limit (since that limit
would satisfy x = x+1).
>
> I was thinking about hyperreals or Conway numbers but couldnt quickly
> derive an answer. Hyperreals seem not have this property.
>
--
G. A. Edgar http://www.math.ohio-state.edu/~edgar/
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