123.3 + 0.1 is 123.3999999999 ?

Erik Max Francis max at alcyone.com
Thu Jun 5 04:17:46 CEST 2003

Andrew Dalke wrote:

> Anyway, so I wish to know which definition of the reals you
> refer to, in the sense that I though all the definitions used (like
> continued fractions) were equivalent to the common notation
> where "0.99999...." does equal 1.

There are all sorts of alternative definitions of the reals which have
differing properties than the reals we've all come to know and love. 
They usually fall under the general category of "non-standard analysis."
I'm not familiar with the particular alternative that the original
poster mentioned, but non-standard analysis can be employed to get all
sorts of weird things, where you have for instance infinities that are
elements of the (non-standard) reals, often called "projected reals"
(and there's a few different ways of doing it).  Same thing's probably
going on here.

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