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(Wish I could find a link to the math problem I'm thinking of)

This one? http://www.mathacademy.com/pr/prime/articles/zeno_tort/index.asp

AHEM

That last line was supposed to be:

The proof for this is particularly neat.

This recursion is beginning to sound like Lewis Carroll's Paradox. (He was a mathematician/logician in his day job.)

Slashdot is not one person. Slashdot is a diverse group of users ...
...
... you seem to think that what's okay for the MPAA is not okay for Slashdot. For you to hold Slashdot to a stricter standard than the MPAA is, quite simply, mind boggling.

What a mind-boggling waterfall of logic.

CC.

Sounds like someone is smoking a little doobie and riffing on Zeno's Paradox

Dude, chill. It's going to be all right.

--Stephen

Helevius

Although the sequence of blackouts is an odd coincidence. Mebbe somebody's playing a trick.

Nah, that's just the way it works. Things might happen at a statistically average rate, but the actual occurrences tend to be disorderly and will appear "clumped". It's a lot like when Mandelbrot noticed that data transmission errors happened to resemble the Cantor set. Nature is disorderly. The attempt to find patterns in the disorder (a.k.a. "affix blame") is an interesting characteristic of humanity.

If they do prove that space is grainy and can measure the size of the grain, will we finally be able to truncate Pi at some point and actually point to its last digit?

Will Zeno's Paradox no longer be a paradox since it would no longer be about traveling an infinite series of infinitely small distances but rather traveling a large finite number of miniscule 'space grains'?

Could the relativity of time be more about different sizes of 'time grains' and a little less about where an observer might be standing? The rate of passage of 'time grains' being universally constant but the size of the grains dependant on local conditions?

Our minds are in a maze full of dark and twisty passages. (At least mine is.)

...and I found this:
"The secret of its making can be rendered somewhat less obscure by examining the grid-paper sketch the artist made in preparation for this lithograph. (picture here)Note how the scale of the grid grows continuously in a clockwise direction. And note especially what this trick entails: A hole in the middle. A mathematician would call this a singularity, a place where the fabric of the space no longer holds together. There is just no way to knit this bizarre space into a seamless whole, and Escher, rather than try to obscure it in some way, has put his trademark initials smack in the center of it."
The whole article can be found here. I didn't see the site, apparently /.ed. Just my $0.02.

...and I found this:
"The secret of its making can be rendered somewhat less obscure by examining the grid-paper sketch the artist made in preparation for this lithograph. (picture here)Note how the scale of the grid grows continuously in a clockwise direction. And note especially what this trick entails: A hole in the middle. A mathematician would call this a singularity, a place where the fabric of the space no longer holds together. There is just no way to knit this bizarre space into a seamless whole, and Escher, rather than try to obscure it in some way, has put his trademark initials smack in the center of it."
The whole article can be found here. I didn't see the site, apparently /.ed. Just my $0.02.

Actually one is Achilles chasing a tortise and the other is a flying arrow is always stationary.

Here is the turtle.

As a matter of interest, you referred to the concept of a "value of infinite that is greater than other black holes". This has little to do with black holes, but it's worth noting that in number theory, there are indeed infinities that are bigger than other infinities. The proof of this is fairly easy to understand - if you're interested, try this page for a very accessible explanation.

You're pretty close there. Aleph0 is the cardinality of the set of all integers, c is the cardinality of the set of all reals. Cantor's diagonalization proof demonstrates that c > Aleph0.

But the exact "value" of c, in relation to other transfinite cardinals was not determined. In particular, its relationship to Aleph1 (which I believe is the cardinality of the power set of Aleph0) is formally undecidable. That is to say, it doesn't make any difference to your system of mathematics if you choose c

It's been a while since I've studied this stuff, but I've found this a decent introduction to the subject.

Nope, not joking. Goedel also had a Completeness Theorem, which states what the original poster says it does -- that first-order predicate logic is complete. However, I disagree with the poster that you can construct FLT as a sentence of first-order predicate calculus, because I don't think you can get the operation of power, among others, out of FOPC. Therefore, FLT is a sentence of elementary number theory which is not a sentence of FOPC, and is therefore, in principle, the sort of thing which might be unprovable.

To prove I'm not smoking crack, I'll note that there are Diophantine representations of FLT and that Greg Chaitin has shown that there are Diophantine equations which are unprovable in Goedel's sense. FLT is clearly not one of them, but Turing's work shows us that we can't actually prove unprovability about a given theorem. So, FLT might have been unprovable.

BTW, it's difficult to give old KG his umlaut, but at least leave him the dignity of an 'e' after the 'o'. Otherwise the English speaking world will start pronouncing him as "Go - dell", which is already beginning to become a problem.