Interesting Continuity QuestionDate: 09/01/2005 at 18:43:05 From: Maggie Subject: Calculus Continuity in Functions Is every function continuous at some point in its domain? I thought that every function didn't have to have a continuous point, therefore not every function would be continuous at some point in its domain, but I'm not sure. Date: 09/02/2005 at 19:10:45 From: Doctor Julien Subject: Re: Calculus Contiunity in Functions Hi Maggie, Thanks for writing! No, not every function has to have a point in its domain where it is continuous. Formal definition aside, continous means the function is "smooth". Take the following function: f(x) = 1 if x is rational -1 if x is irrational This function "jumps around" from 1 to -1, and has no points that are continous anywhere! You can see a picture of a similar function here: DirichletFunction http://mathworld.wolfram.com/DirichletFunction.html Does this help? - Doctor Julien, The Math Forum http://mathforum.org/dr.math/ |
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