Dear Colleagues,
The BanachTarski Paradox, which suggests that the usual foundations of mathematics allow one to decompose a solid ball into parts and reassemble the parts into two solid balls congruent to the original, can be dealt with in a way that resolves this paradox but as the article below shows creates a new paradox in its place.
http://stanwagon.com/public/TheDivision ... rWagon.pdf
The article is somewhat technical but raises though provoking concerns about the foundations of mathematics that we are familiar with.
Regards,
Joe
Replacing one paradox with another
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Replacing one paradox with another
Joseph Malkevitch
Department of Mathematics
York College (CUNY)
Jamaica, New York 11451
email:
malkevitch@york.cuny.edu
web page:
http://york.cuny.edu/~malk
Department of Mathematics
York College (CUNY)
Jamaica, New York 11451
email:
malkevitch@york.cuny.edu
web page:
http://york.cuny.edu/~malk
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