(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Where is the function f(x) continuous?

f(x) =

x, if x is rational

0, if x is irrational

2. Relevant equations

3. The attempt at a solution

Is this correct?: I approach some c =/= 0, 1st through x's that are rational

and prove there is the limit c, and then approach through x's that are irrational and prove that the limit now cannot be c, that now I can conclude that the limit at c does not exist, and hence the function is not continuous at any c=/=0?

If no, why, and in what other way must I solve it then? If yes, plz try to explain as rigourously as you can why this can be done. Remind you though, don't get technical above 2nd year in which I am. Thank you.

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# Homework Help: Continuity of Dirichlet looking function

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