Timeline for Are real numbers countable in constructive mathematics?
Current License: CC BY-SA 2.5
8 events
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| Jul 12, 2010 at 14:05 | comment | added | Vag | @Daniel Mehkeri: Thanks, I'm working out your answer slowly. Answers given fueled my learning for a many weeks :) | |
| Jul 11, 2010 at 18:07 | comment | added | Daniel Mehkeri | @Vag: I would point back to the countable/subcountable distinction. The real numbers are not countable, but they are subcountable from a certain constructive point of view, as I said in my answer. That means there is a partial surjection F from the integers to the reals. So in a sense we can write them all down: for every real x there is an integer n such that F(n)=x. Of course there is no procedure to decide for a given n whether F(n) is defined. | |
| Jul 11, 2010 at 14:40 | comment | added | Vag | For intuition breaking point of view I've found interesting this conjunction: "Every real is approximable by unbounded computation, i.e. `may be written down', but it is unable to write down all reals." | |
| Jul 7, 2010 at 7:30 | comment | added | Vag | My motivation while asking was: "I want to know ALL about this interesting chain of reasoning" but not "My intuition stalemates me, help!". | |
| Jul 7, 2010 at 2:04 | comment | added | Peter Boothe | I suppose I am talking to the computer scientists I have known who have strayed from the constructive countable mathematics of most CS courses into the domain of the reals without ever having taken a real analysis course. The original question struck me as being very similar to others that I have fielded (as a half math/half CS undergrad) from people in that category. | |
| Jul 6, 2010 at 16:08 | comment | added | Dan Piponi | I wonder who you are talking about when you say that their "intuition breaks down" and that their "intuition is almost entirely unsuitable for reasoning in this domain". | |
| Jul 6, 2010 at 15:44 | history | edited | Peter Boothe | CC BY-SA 2.5 |
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| Jul 6, 2010 at 13:27 | history | answered | Peter Boothe | CC BY-SA 2.5 |