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!

#Calculus #Limits #Continuity #HelpMe! #Nowherecontinuous

Easy Math Editor

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Comments

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

Calvin Lin Staff - 6 years ago

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 - 5 years, 12 months ago

Lucy Oakley - 5 years, 6 months ago

Hey.

Raj Magesh - 5 years, 6 months ago

How are you

Lucy Oakley - 5 years, 6 months ago

@Lucy Oakley – Great, you?

Raj Magesh - 5 years, 6 months ago

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

Harshita Arya - 6 years ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$