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Cyan2 comments on Artificial Addition - Less Wrong

36 Post author: Eliezer_Yudkowsky 20 November 2007 07:58AM

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Comment author: Cyan2 22 November 2007 07:48:45PM 1 point [-]

Benoit,

In the decimal numeral system, every number with a terminating decimal representation also has a non-terminating one that ends with recurring nines. Hence, 1.999... = 2, 0.74999... = 0.75, 0.986232999... = 0.986233, etc. This isn't a paradox, and it has nothing to do with the precision with which we measure actual real things. This sort of recurring representation happens in any positional numeral system.

You seem very confused as to the distinction between what numbers are and how we can represent them. All I can say is, these matters have been well thought out, and you'd profit by reading as much as you can on the subject and by trying to avoid getting too caught up in your preconceptions.