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Einfach
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Einfach
1,448 posts
Nomad

It seems to make absolutely no sense whatsoever, so if anyone out there understands it, could they please explain it here?

http://www.ms.uky.edu/~lee/banach.pdf

  • 16 Replies
Kevin4762
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Kevin4762
2,420 posts
Nomad

If I knew what the math meant, I'm pretty sure it would make sense, but I could be mistaken.

Haki7
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Haki7
58 posts
Nomad

I believe it says some mumbo-jumbo is a paradox because it doesn't follow the other mumbo-jumbo.

Einfach
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Einfach
1,448 posts
Nomad

I believe it says some mumbo-jumbo is a paradox because it doesn't follow the other mumbo-jumbo.


You can prove it - but I don't get it...Can someone explain in English how you prove it so I could understand it? This isn't for school or anything - this is for my own understanding, because there can be no contradictions in my universe...

If there wasn't a proof for this, I would consider it complete BS.
Maverick4
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Maverick4
6,800 posts
Peasant

I'm still trying to figure out why the symbol for gamma-rays have been thrown in their. But *I think* its saying that if you spread out the mass of any given object, over a great enough area, you can create an object of infinite size.

Probaly wrong, but than I don't know any of the math thats in the PDF.

Squidbears
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Squidbears
626 posts
Nomad

It says that you can decompose a ball into 6 pieces and reassemble them to make 2 balls of the same size as the original ball

Einfach
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Einfach
1,448 posts
Nomad

@Squidbears - I got that much. I want to know the mathematical justification.

Squidbears
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Squidbears
626 posts
Nomad

oh my bad, yea.. the mathematical part doesnt really make sense to me.. but this paradox kinda destroyed my views of volume

Einfach
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Einfach
1,448 posts
Nomad

Anyone who understands this, please post...I need to know...

Einfach
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Einfach
1,448 posts
Nomad

http://www.kuro5hin.org/story/2003/5/23/134430/275

nevermind...I found an explanation. The paradox itself assumes an infinitely divisible sphere and the axiom of choice.

Squidbears
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Squidbears
626 posts
Nomad

so its purely mathematical? and you cant do it in real life... makes more sense now

Einfach
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Einfach
1,448 posts
Nomad

so its purely mathematical? and you cant do it in real life... makes more sense now


Both statements are true, but putting them together seems to imply that one implies the other.

You can't do it in real life because it assumes an infinitely divisible shape, whereas all matter is divisible into small units.
Maverick4
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Maverick4
6,800 posts
Peasant

Eh... I was close. And thanks for the enlightenment. I was very puzzled over this.

Squidbears
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Squidbears
626 posts
Nomad

whoever thought of this had too much time on their hands i think... but its a really interesting thought

Kevin4762
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Kevin4762
2,420 posts
Nomad

The article says that it is a mathematical sphere, not a physical sphere. I have no idea what's the difference. All I know is that there is a Universal Set in the math and that the have the symbol for mass in there.

Einfach
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Einfach
1,448 posts
Nomad

The article says that it is a mathematical sphere, not a physical sphere. I have no idea what's the difference. All I know is that there is a Universal Set in the math and that the have the symbol for mass in there.


A mathematical sphere is infinitely divisible - it is a perfect sphere and it contains an infinite number of points.

Thus making the Banach-Tarski paradox weird, but a little less weird.
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