Continuity of Dirichlet looking function

daolian89 · Mar 18, 2011

Homework Statement

Where is the function f(x) continuous?

f(x) =
x, if x is irrational

0, if x is rational

Homework Equations

The Attempt at a Solution

SVXX · Mar 18, 2011

The function gives 0 output (the Y axis) for all rational inputs and the input itself for irrational inputs. Then if I'm not wrong, the irrational points are points of discontinuity and the function is continuous everywhere else.

Continuity of Dirichlet looking function

Homework Statement

Homework Equations

The Attempt at a Solution

Discussion

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Continuity of Dirichlet looking function

Homework Statement

Homework Equations

The Attempt at a Solution

Discussion

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