"Paul Lutus" <nospam@nosite.zzz> wrote in message news://XLOO7.232748$dk.15586616@bin1.nnrp.aus1.giganews.com... > "The Scarlet Manuka" <sacha@maths.uwa.edu.au> wrote in message > news://9ufdos$nf9$1@fang.dsto.defence.gov.au...
> > I said: The term "number system" is not well-defined, and it would be > > unwise to define it in such a way as to exclude the extended real numbers. > Clearly an argument in favor of the extended reals as the default number > system.
No. It is an argument in favour of the extended reals being a number system. Nothing more. It is not to your credit that you appear not to understand this extremely simple point.
> > In any case, the simple fact that all those pages could be taken to > > refer to several different number systems refutes your claim that > > they define a default number system. For instance, they could (mostly) > > be referring to any of Z, Q, R, or C. These are all different number > > systems. > They all have something in common. They all exclude +-infinity, and they all > assert or imply that this is a property of a default number system.
If what they say applies equally well to many different number systems, how can you argue that they establish a default? If they establish a default, it must surely be possible to deduce what that default is.
