Changes

I'm fine with your edits (I would argue that decimal representations are always infinite but this may be a nitpick). The main causes of the pain were the previous article insisting that the reals contain "infinite values" and the notion that the real numbers *exclude* anything (since if one wants to talk about them that way, one might as well say they exclude cows and deities). Regarding your other comments, I'm not sure of a general name for the procedure, however the motivation for going to the reals that a mathematician would most likely give is that one wants to be able to take limits. As for infinities, that's complicated and can be dealt with in a variety of different ways depending on what one means by infinity. Wikipedia has a few good articles on these topics. I would recommend [http://en.wikipedia.org/wiki/Cardinal_arithmetic cardinal arithmetic] [http://en.wikipedia.org/wiki/Ordinal_number ordinal number] [http://en.wikipedia.org/wiki/Extended_reals extended reals] and [http://en.wikipedia.org/wiki/Surreal_number surreal numbers] as different examples of ways of incorporating infinity. [[User:JoshuaZ|JoshuaZ]] 19:26, 24 February 2007 (EST)

I'm fine with your edits (I would argue that decimal representations are always infinite but this may be a nitpick). The main causes of the pain were the previous article insisting that the reals contain "infinite values" and the notion that the real numbers *exclude* anything (since if one wants to talk about them that way, one might as well say they exclude cows and deities). Regarding your other comments, I'm not sure of a general name for the procedure, however the motivation for going to the reals that a mathematician would most likely give is that one wants to be able to take limits. As for infinities, that's complicated and can be dealt with in a variety of different ways depending on what one means by infinity. Wikipedia has a few good articles on these topics. I would recommend [http://en.wikipedia.org/wiki/Cardinal_arithmetic cardinal arithmetic] [http://en.wikipedia.org/wiki/Ordinal_number ordinal number] [http://en.wikipedia.org/wiki/Extended_reals extended reals] and [http://en.wikipedia.org/wiki/Surreal_number surreal numbers] as different examples of ways of incorporating infinity. [[User:JoshuaZ|JoshuaZ]] 19:26, 24 February 2007 (EST)