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Re: What is infinity minus one?
Posted:
Oct 14, 2004 8:32 AM
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>Further, I googled for "system of extended real numbers" and achieved
>only one result, unrelated to this. So I will assume that this is not
>the name I should be looking for when attempting to learn. What should I
>search for in order to get more useful results?
You can start with Cantor's theory of transfinite numbers
OR
you can try the HYPER-REAL number system.
Please note, that while both are mathematical systems that allow
reasonable investigations into properties of "infinity", they are
not the same. In a simplistic sense, Cantorian transfinites are
more like integers, while the hyper-reals are more like the reals.
Thus while many things are the same in both systems, some things
are different.
I would suggest that to get a "handle on infinity", the Cantorian
transfinites are easier to deal with rigorously. However, if you
want to apply to understanding real-world idealizations, e.g., Dirac
delta functions, the hyper-reals are more useful, however maintaining
rigor requires more effort.
YMMV
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