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See the last few pages of [http://faculty.uml.edu/jpropp/305/10.30.doc Excellent proof] for proofs of continuity on the irrationals and discontinuity on the rational numbers.
A second, <small><small>[http://www.math.washington.edu/~morrow/334_10/thomae.pdf Proof but with a Mistake] is easier to follow
but needs to be rearranged. It defines m, then later assumes a property about m.
A better ordering starts,
:Let epsilon > 0, Let m be an integer such that, 1/m < epsilon.
The second proof may have other mistakes. It could use a clearer transition from proof of continuity proof of discontinuity. Replacing variables in the 2nd half to prevent confusion with the first half, would also be useful.
The next step would be to investigate copyright issues for these proofs. Or possibly rewrite them to avoid copyright issues.</small></small>
--[[User:Nickalh50|Nickalh50]] ([[User talk:Nickalh50|talk]]) 19:41, 14 March 2011 (UTC)
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