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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
1 year, 7 months ago

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Do you know what is the delta epsilon definition of a limit? Calvin Lin Staff · 1 year, 7 months ago

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@Calvin Lin 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 · 1 year, 7 months ago

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hi Lucy Oakley · 1 year, 1 month ago

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@Lucy Oakley Hey. Raj Magesh · 1 year, 1 month ago

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@Raj Magesh How are you Lucy Oakley · 1 year, 1 month ago

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@Lucy Oakley Great, you? Raj Magesh · 1 year, 1 month ago

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These are called drichlet functions and these are continuos when both equations are equal Harshita Arya · 1 year, 7 months ago

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