Comic Discussion > QUESTIONABLE CONTENT
WCDT 2126-2130 (20-24 Feburary 2012) QC in SPAAAAAAACE! Week 5
Carl-E:
Phsst! Collectors.
[checks his manhatten depression glass and notes the remaining pieces needed for a complete set]
Skewbrow:
--- Quote from: Is it cold in here? on 24 Feb 2012, 12:36 ---There's something floating around the net that says "The Tao of mathematics: the numbers you can count are not the real numbers".
--- End quote ---
:-D I like that quote. Even though it is too open-to-interpretation to have a precise meaning. My take is that whoever said that meant that "the numbers you can count form a small minority among all the real numbers", but admittedly that is a dull way of putting it.
Edit: Should have said "... the numbers you can compute"
celticgeek:
The set of integers is countably infinite. The set of real numbers is uncountably infinite.
Skewbrow:
True. What I was aiming at is that the set of computable numbers is also countably infinite, and hence a small minority among the real numbers. I should have foreseen the confusion that necessarily results from using "countable" and "computable" interchangably in a situation, where the correct interpretation of terms is meaningful, likely to happen, and contradicts with my intended meaning. Sorry about that.
So the tl; dr; version (math forces these upon us - otherwise confusion will arise). Most numbers cannot be computed. IOW it is impossible to write a computer program that would print out the decimals of that number. Even if we would allow the program to run from here to eternity (like a simple program printing out 1/3 would just endless keep on printing out more and more 3s in an endless loop). Or yet in other words: most real numbers exist only for the purpose of making the math playground complete and safe for the players.
Akima:
--- Quote from: Skewbrow on 24 Feb 2012, 21:55 ---Even though it is too open-to-interpretation to have a precise meaning.
--- End quote ---
What do you expect?:
"The Tao that can be spoken is not the eternal Tao
The name that can be named is not the eternal name."
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