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Let f be the Thomae function aka the popcorn function. Use the epsilon-delta to prove that f is continuous for all irrational numbers and discontinuous for all rational numbers.

Martin Sleziak
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jess_001
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    Welcome to Math.SE! Please expand your post to add your thoughts or progress on the problem so we can help you where you are stuck. – Peter Woolfitt Jan 22 '15 at 07:44
  • I think it will be in sequential approach.. – Empty Jan 22 '15 at 08:40
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    BTW exactly the same question was posted on the same day by another user. Now the question is deleted, here is link for 10k+ users: http://math.stackexchange.com/questions/1114732/help-with-proof-using-epsilon-delta-please – Martin Sleziak Feb 24 '15 at 11:27
  • @jess_001 If both accounts belong to you, you can merge them following the instruction given here. – Martin Sleziak Feb 24 '15 at 11:31
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    I will also point out that you can easily find many posts about this problem, simple using Google for some reasonable search phrase. For example: http://math.stackexchange.com/questions/207118/, http://math.stackexchange.com/questions/1036269/, http://math.stackexchange.com/questions/530097/, http://math.stackexchange.com/questions/860082/, ... – Martin Sleziak Feb 24 '15 at 11:34

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