Subject:
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Re: 22/7 & infinities (was: Re: The nature of the JC god, good or evil?)
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Newsgroups:
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lugnet.off-topic.geek
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Date:
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Wed, 25 Aug 1999 02:49:24 GMT
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Viewed:
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1266 times
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In lugnet.off-topic.debate, Todd Lehman writes:
> [...] 22/7 is just a rough approximation to pi; [...]
> Another cool one is 333/106, which happens to come within ~.0026% of the
> actual value:
> 333/106 = 3.141509433962...
The "much better" one I heard was 355/113:
355/113 = 3.141592920353...
which comes within ~0.000008 percent...
> OTOH, irrational numbers like sqrt(2), e, and pi are not part of a countable
> infinity because (it's been proven that) there is no way to enumerate the
> irrational numbers.
It's interesting to note, however, that there are important sets of numbers
that include these irrational numbers and are countable infinities -- such as
the set of all finite-length Maple expressions (-:
> So some infinities are bigger infinities than others. [...]
I am so overwhelmed by all the different ways of defining transfinite numbers
that I've almost given up. The Cantor system is complicated enough, but then
there's Conway's system based on the hackenbush game of labeled graph
truncation (or something like that -- see? that's why I gave up! :-)
I'm content with mere staggeringly huge finite numbers, such as you'll find on
http://www.mrob.com/largenum.html (just don't try bulk ordering
Ackermann(Skewes-number) blue tiles)
> It's true that irrational numbers like sqrt(2) and pi go on forever and ever
> in their decimal expansions, and that the entire universe working forever
> and ever to compute the entire sequence would never complete. [...]
I'm still not convinced that the entire universe is actually finite. I like to
hold out the possibility that there's more to it than anyone will ever find...
and I'm not even talking about the spiritual possibilities, which are
a-whole-nother matter...
> [3] Is mathematics part of the universe?
Yeah, there's another possibility. Forgot about that one (-:
- Robert Munafo http://www.mrob.com/
LEGO: TC+++(8480) SW++ #+ S-- LS++ Hsp M+ A@ LM++ YB64m IC13
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