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Talk:Set of real numbers: Difference between revisions
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:: @Dkf: I'll reword the datatype thing. --[[User:Ledrug|Ledrug]] 11:16, 30 September 2011 (UTC)
:This depends on an implementation for "real numbers" and it's not clear whether floating point is considered adequate in this role. --[[User:Rdm|Rdm]] 17:57, 30 September 2011 (UTC)
: The name of the task is somewhat unfortunate, since only a (rare IMO) subset of the sets of real numbers are included. I'd think that "intervals of real numbers" would be more accurate. Any other ideas for names?
: Otherwise the task seems fine to me.
: [[User:CRGreathouse|CRGreathouse]] 08:17, 21 November 2011 (UTC)
:: Indeed, the number of sets of real numbers describable by this task is countable; whereas the number of sets of real numbers is uncountable. (In fact, the real numbers are already uncountable; its power set has an even bigger cardinality than the real numbers.) So, in fact, this task covers a measure-zero subset of the sets of real numbers. --[[User:Spoon!|Spoon!]] 10:07, 21 November 2011 (UTC)
==Wolfram Mathworld and Perl==
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::::::::: I don't really want to specify a test case for empty test. To make available operations more or less complete, you need one of the three (besides ones already in the mandetory part): is empty, set equality, or is subset. Provide any one, and the other two can be easily constructed through other binary operators. It just seemed to me that empty test is likely the least amount of work. And since length calculation would require one of them (or prove me wrong), a test case isn't necessary. As to how you do any of the required or optional task, I'm not really concerned: if all the basic methods are available, the implementation should be reasonably usable, that's all that matters. --[[User:Ledrug|Ledrug]] 01:37, 5 October 2011 (UTC)
:::::::::: As I said before, I am doing my length calculation without any of those three. The data structure I use does not concern itself with the distinction between open and closed interval and thus is not capable of supporting is empty nor set equality nor is subset. That said, the version with empty set support does have enough information to compute length -- I'll try posting an implementation of that for comparison. --[[User:Rdm|Rdm]] 10:39, 5 October 2011 (UTC)
::::::::::: No, but you are using a way to iterate through the innards of the set implementation, which is what you need to implement any of the three. The reason the empty test can't be done with only the "has element" test is that a real set is uncountable, so you can't even conceptually exhaustively test a list of candadites for insideness via a (potentially infinite) loop. --[[User:Ledrug|Ledrug]] 23:17, 5 October 2011 (UTC)
:::::::::::: If partial innards, which are not sufficient to satisfy the requirements of the membership test part of the task, count, then yes. --[[User:Rdm|Rdm]] 23:34, 5 October 2011 (UTC)
:::::::::: Ok, that's done. It's more than twice as much code, from the same starting point. The number in the answer is also slightly, which surprises me. I did not think that there were enough floating point subtractions involved to accrue that big of an error. --[[User:Rdm|Rdm]] 20:14, 5 October 2011 (UTC)
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