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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: 937 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 onetoone 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: 7,116 Thanks: 2369 Math Focus: Mainly analysis and algebra 
Presumably that could or should read 'infinite set'.

November 7th, 2014, 03:23 PM  #4 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  
November 7th, 2014, 04:30 PM  #5 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,116 Thanks: 2369 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  
Senior Member Joined: Jan 2014 From: The backwoods of Northern Ontario Posts: 371 Thanks: 68  Quote:
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 
Senior Member Joined: Jul 2009 Posts: 136 Thanks: 0  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? 

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