From: Yuri Tzara Date: 2010-11-26T05:19:18+09:00 Subject: Re: Ruby 1.8 vs 1.9 Phillip, regarding defining 1/0 you said, > It cannot be infinity. It does, quite literally not compute. There's > no room for interpretation, it's a fact of (mathematical) life that > something divided by nothing has an undefined result. It doesn't > matter if it's 0, 0.0, or -0.0. Undefined is undefined. Nonsense. These claims are roundly refuted by http://en.wikipedia.org/wiki/Extended_real_number_line#Arithmetic_operations IEEE floating point operations on oo and -oo match those *precisely*. IEEE models the extended real number line. > I'm quite aware that IEEE 754 defines the result of x_0/0 as > infinity. That is not, however, correct *in a mathematical sense*. Nonsense. Infinity defined this way has solid mathematical meaning and is established on a firm foundation, described in the link above. > The IEEE standard, however, does *not* define how mathematics work. > Mathematics does that. In math, x_0/0 is *undefined*. It is not > infinity... Right, IEEE does not define how mathematics works. IEEE took the mathematical definition and properties of infinity and incorporated it into the standard. Clearly, you were unaware of this and repeatedly ignored the information offered to you about it. > Quote Wikipedia: > "Unlike most mathematical models of the intuitive concept of 'number', > this structure allows division by zero [snip formula], for nonzero a. > This structure, however, is not a field, and *division does not retain > its original algebraic meaning in it*." > > Emphasis mine. That sentence. You evidently do not understand what it means. It does not mean what you think it means. > Your argument is also called "moving the goal posts". But even if > we consider it: non-algebraic systems are not something 99% of all > non-professional-mathematicians engage in (so, we can toss in a "no > true Scotsman" fallacy into the bargain). Nonsense. Every person who has obtained a result of +oo or -oo from a floating point calculation has engaged in it. A result of +oo or -oo is often a meaningful answer and not an error. And even when it is an error, it gives us information on what went wrong (and which direction it went wrong in). It's entertainingly ironic that you attribute "moving the goalposts" and the no true Scotsman fallacy to the wrong person in this conversation. Thanks for another great demonstration of the Dunning-Kruger effect. -- Posted via http://www.ruby-forum.com/.