zkeletenz's Comments
Pax: Yes, I am confident about my logic, but I am not a mathematician.
Thanks for the support, Hoax.
Thanks for the support, Hoax.
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To respond more specifically to your reasoning, the example you provide is unfair, because it happens to coincide with the limits of the decimal system. 8/2 works with the decimal system perfectly, because it divides evenly by integers. The same cannot be said for 1/3.
To explain it on its own terms, with no need for analogy. Let's say that you have a rifle with 10 horizontal aiming positions. Now, you have a target that lands at position 4 (8/2nds from your example) position. Can you hit it? Yes.
But can you hit a target at the 1/3rd horizontal position? Unfortunately, no. You need a better scope. You can change to a 100-point scope, or 1000 or 1 google plex. But you still have the same problem.
This is not a paradox - it is perfectly consistent. It is just another way of saying that you have a digital scale (10-point, 100, 1000, or whatever digital limit you are using). An infinitely-repeating digital expression will never perfectly express a fraction that does not divide evenly. That's what infinite repetition means - it is NOT FINITE.
To explain it on its own terms, with no need for analogy. Let's say that you have a rifle with 10 horizontal aiming positions. Now, you have a target that lands at position 4 (8/2nds from your example) position. Can you hit it? Yes.
But can you hit a target at the 1/3rd horizontal position? Unfortunately, no. You need a better scope. You can change to a 100-point scope, or 1000 or 1 google plex. But you still have the same problem.
This is not a paradox - it is perfectly consistent. It is just another way of saying that you have a digital scale (10-point, 100, 1000, or whatever digital limit you are using). An infinitely-repeating digital expression will never perfectly express a fraction that does not divide evenly. That's what infinite repetition means - it is NOT FINITE.
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Thankyou, professor, this "namecalling" you have exhibited is yet another example of approximated terms to express more complex concepts. In the same way that your general, unreasoned term "Poppycock" gives insufficiently particular information concerning the concept you seek to advnace, the decimal expression .333 (repeated infinitely) gives insufficient expression to the concept of dividing into 1/3rd.
/takes his bow
//knows he is a wise-a&&
/takes his bow
//knows he is a wise-a&&
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The mistake here is assuming that the decimals .333... and .666... are accurate expressions of 1/3 and 2/3, respectively. They are not. They are simply the closest digital expressions can come to expressing analog. And that's why your CD/MP3 will never sound as good as granpa's phonograph. Sorry!
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Mr. Lombard: I actually thought of the concept when I was a fetus. So, as they say in Intellectual Property parlance, I "swear behind your conception date." :)