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 November 7th, 2014, 12:29 PM #1 Senior Member   Joined: Jul 2009 Posts: 136 Thanks: 0 Help with Math Statement about Art One of the judges for the Math Art show asked me to clarify or strengthen the math behind the art. Maybe someone can help me with this? I was thinking that this might be the Galileo paradox but unsure. Well, if you can then let me know; thanks! "An infinite amount of radii in any circle, when extending beyond the boundary of that circle, begets another infinite series of radii so that an infinity transforms into a series of infinities, ad infinitum."
 November 7th, 2014, 01:08 PM #2 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms The Galileo paradox is that a set can be equinumerous to one of its proper subsets -- the two can be put in a one-to-one relationship with each other, even though some elements are missing from one set. Does your artwork show this?
 November 7th, 2014, 02:40 PM #3 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,551 Thanks: 2554 Math Focus: Mainly analysis and algebra Presumably that could or should read 'infinite set'.
November 7th, 2014, 03:23 PM   #4
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Quote:
 Originally Posted by v8archie Presumably that could or should read 'infinite set'.
Yes, it only happens for infinite sets. Whether it happens for all infinite sets is a somewhat more delicate matter than you might imagine -- but for practical purposes the answer is "yes".

 November 7th, 2014, 04:30 PM #5 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,551 Thanks: 2554 Math Focus: Mainly analysis and algebra Now you mention it, I can imagine that uncountable sets present problems in as much as it is rather difficult to prove that all members of both sets are part of the map.
November 7th, 2014, 06:07 PM   #6
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Quote:
 Originally Posted by CR Greathouse The Galileo paradox is that a set can be equinumerous to one of its proper subsets -- the two can be put in a one-to-one relationship with each other, even though some elements are missing from one set
.

I tried to think of an example. I came up with this example: one set could be the set of all positive rational numbers. And the subset could be the set of all positive rational numbers between 1 and 2.

November 7th, 2014, 07:33 PM   #7
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to CR, V8, and Timios

Thanks very much to all!

I attached the drawing, it shows various spheres nested in each other, presenting the radii (presumed infinite amount) within spheres of other radii. Do you think that works?
Attached Images
 Transformation of Infinity.jpg (98.0 KB, 3 views)

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