Felix~ You are correct that the sequence of numbers
0.9 0.99 0.999 ... asymptotically approaches 1; however, the number 0.9999... (with an infinite number of 9s) is equal to 1. The formal proof of this is fairly tricky as the definition of the real number is usually done as an equivalence class of Cauchy sequences; a simplified version of the proof can be thought of as follows: For any two real numbers *a* and *b* there exists an infinite number of real numbers *c *such that *a < c < b*. However, there do not exist any numbers between 0.99999... and 1, thus they must be same number. As it turns out, it took mathematicians a long time to nail down formally exactly what we naively think of as "numbers". Matt On Wed, Oct 13, 2010 at 6:27 PM, Felix H. Dahlke <f...@ubercode.de> wrote: > On 13/10/10 22:28, David Sletten wrote: > > > > On Oct 12, 2010, at 5:44 PM, Brian Hurt wrote: > > > >> For example, in base 10, 1/3 * 3 = 0.99999... > > > > It may seem counterintuitive, but that statement is perfectly true. > > 1 = 0.9999... > > > > That's a good test of how well you understand infinity. > > I'm clearly not a mathematician, but doesn't 0.99999... asymptotically > approach 1, i.e. never reaching it? How is that the same as 1? > > -- You received this message because you are subscribed to the Google Groups "Clojure" group. To post to this group, send email to clojure@googlegroups.com Note that posts from new members are moderated - please be patient with your first post. To unsubscribe from this group, send email to clojure+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/clojure?hl=en
