"Bill Page" <[EMAIL PROTECTED]> writes: | On Tue, Apr 8, 2008 at 10:24 PM, Gabriel Dos Reis wrote: | > | > | On Tue, Apr 8, 2008 at 8:59 PM, Gabriel Dos Reis wrote: | > | > Bill Page writes: | > | > | > | > | I can not agree. Because something cannot always be computed | > | > | does not mean that it is therefore ill-defined. This is especially | > | > | true in mathematics. | > | > | > | > I believe you're putting confusing the issues. Function equality | > | > is well-defined in classic mathematics (set theoretical). But | > | > that definition is almost useless from algorithmic perspective. | > | > | > | | > | I do not think "almost unless" is synonymous with ill-defined even | > | from an algorithmic perspective. | > | > So? | | So, I was waiting for you to present the reason why earlier you said: | "From computational (there algorithmic) perspective, function equality | is ill-defined." But so far I have been disappointed.
Then, I'm sorry for you. [...] | You have injected the words "hack" and "worship" here but I do not | think they are appropriate. What reason do you have to believe that I | worship anything in particular? Because you have not given the substance that the category theory must work with in the context that is of interest to us. You have only posted links to stuff -- largely known to the audience -- which are *axiomatic* in nature. You have carefully avoided giving any rigorous definition that can be tested -- that is not science. | When have I ever proposed a simple | "hack" just to make something work without asking why it works the way | that it does? Your `characterization' of equality of functions :-) [...] | > Then we just have to agree to disagree. I don't believe in worship in | > category theory. I do believe category is an extremely sophisticated | > and powerful tool... when one has actual *matter* to work with. | > | | I do not believe in "worship" of category theory either but I do not | understand what you mean by "actual matter". What counts as *matter* | to you? The substance that the `category theory' is to be applied to. -- Gaby ------------------------------------------------------------------------- This SF.net email is sponsored by the 2008 JavaOne(SM) Conference Don't miss this year's exciting event. There's still time to save $100. Use priority code J8TL2D2. http://ad.doubleclick.net/clk;198757673;13503038;p?http://java.sun.com/javaone _______________________________________________ open-axiom-devel mailing list open-axiom-devel@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/open-axiom-devel
