PUZZLE: Let EC(X) denote the Euler characteristic of X. Solve for X: EC(X) = X --Dan P.S. Thanks to Evan O'Dorney for pointing out a case I had overlooked. Sometimes the brain has a mind of its own.
Do you mean solutions of the following form? "A torus is shaped like a 0, and has an Euler characteristic of 0." Otherwise, it doesn't seem to make much sense, as EC() has a domain of topologies and a codomain of integers, which have no intersection. Or are you referring to another meaning of 'Euler characteristic', which I haven't heard of? Sincerely, Adam P. Goucher
PUZZLE: Let EC(X) denote the Euler characteristic of X.
Solve for X:
EC(X) = X
--Dan
P.S. Thanks to Evan O'Dorney for pointing out a case I had overlooked.
Sometimes the brain has a mind of its own.
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On Wed, Apr 13, 2011 at 12:59 PM, Dan Asimov <dasimov@earthlink.net> wrote:
PUZZLE: Let EC(X) denote the Euler characteristic of X.
Solve for X:
EC(X) = X
--Dan
The Euler characteristic is a number, whereas X is at least a set. Can you clarify? -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
Via the fixpoint combinator: X = Y(EC) = EC(Y(EC)) On Wed, Apr 13, 2011 at 12:59 PM, Dan Asimov <dasimov@earthlink.net> wrote:
PUZZLE: Let EC(X) denote the Euler characteristic of X.
Solve for X:
EC(X) = X
--Dan
P.S. Thanks to Evan O'Dorney for pointing out a case I had overlooked.
Sometimes the brain has a mind of its own.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
participants (3)
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Adam P. Goucher -
Dan Asimov -
Mike Stay