I always hated Zeno's crap. It's what smug mathematicians used to harass me with when I was doing pre-calculus in the sixth grade.
I'm glad someone else isn't putting up with it.
|Gamara II |
Spoiler: Zeno sux
Maths... the most useless of all sciences.
In terms of the Tortoise, Achilles, and Infinity; I always preferred Lewis Carroll's dialogue over Zeno's.
In terms of smug mathematician tricks to play on middle school kids, I defiantly preferred Zeno's dialogue over that ridiculous .999... = 1
We get it nerd, decimal notation is not always a perfect way to represent numbers. You are not a fucking genius for pointing this out.
edit: I am bleary-eyed and did not utilize spell-check properly:
defiantly = definitely
"fucking convergence of a geometric series, how does it work?"
well, one-ninth is 0.111...
9 x 1/9 = 1
x = 0.999...
10x = 9.999...
10x - x = 9.999... - 0.999...
9x = 9.0
x = 1
but you could also use geometric convergence, the series converges to .9/1-.1, or .9/.9, which equals 1.
I'm not sure what's more "perfect", as any base system is going to run into problems of infinity using real numbers. I'm just as curious as anyone else for wondering how I'd count if I were missing some fingers (or maybe grew some extra ones), but binary, base 3, octal, hex, whatever, it doesn't really change what the numbers themselves "are", just the symbols used.
Actually I can see how the tortoise thing is more fun to think about. The .999... thing leaves you with the impression that some trick has been done with the symbols themselves.
That's not the case... as king pointed out, it's a property of infinite series rather than any particular number system, but still, Zeno's paradox gives you something a little more concrete to think about.
Fun math game: try and notice how often people fall prey to the birthday paradox or the gambler's fallacy. But don't correct them, because they will hate you for knowing some math.
This is what mathematicians actually believe.
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