On Mon, 9 May 2011, Bryan Jurish wrote:
sqrt(2) ? exp(1) ? pi ? ... certainly each of the "usual suspects" has a discrete specification, but I've always been a bit suspicious of the hardcore constructionist approach to irrational numbers
Of course, infinitely long patternless sequences of digits make a lot more sense (???).
(while at the same time finding it extremely attractive to my engineering/hacker instincts). ok, so these are probably not "measurable" in the sense you mean either, but they are *thinkable*, and that (I think) is the whole point (or as it were, the whole hypotenuse, curve, circle, etc) ;-)
or rather, it's the whole tangent that gets you away from the topic ;) There are lots of facts about the universe that are not knowable.Analogue audio theory is made with «Real» numbers because that's what fitted best to explain the experiments that had been made. Irrational numbers are an artifact of our manners of thinking, and uncountable sets of «Real» numbers are even more so artifacts.
It doesn't mean that those artifacts don't exist in the physical world, it means that we had to invent those concepts by ourselves because we can't perceive them from the physical world.
_______________________________________________________________________ | Mathieu Bouchard ---- tél: +1.514.383.3801 ---- Villeray, Montréal, QC
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