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Help Me! Functions, limits and continuity

Hey guys,

Today I came across a question about the function \(f(x)\), which takes the value \(x\) when \(x \in Q\) and the value \(1-x\) when \(x \notin Q\). Is this function continuous at any point?

I thought that \(f(x)\) would be continuous at \(x=0.5\) since the left and right hand limits seem to approach \(0.5\) near \(x=0.5\).

Am I correct? If so, why? If not, why?

Thanks!

Note by Raj Magesh
2 years, 6 months ago

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Do you know what is the delta epsilon definition of a limit?

Calvin Lin Staff - 2 years, 6 months ago

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Thanks a lot! I went through the wiki and worked out the answer to my question. The epsilon-delta definition is broader than the one I learnt in school...

Raj Magesh - 2 years, 6 months ago

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hi

Lucy Oakley - 2 years ago

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Hey.

Raj Magesh - 2 years ago

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How are you

Lucy Oakley - 2 years ago

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@Lucy Oakley Great, you?

Raj Magesh - 2 years ago

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These are called drichlet functions and these are continuos when both equations are equal

Harshita Arya - 2 years, 6 months ago

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