A function ? 2

Calculus Level 3

Does there exist a function defined on the reals which is continuous at only one point?

Impossible to Say No This Question Does Not Make Sense Yes

Christopher Criscitiello by Christopher Criscitiello , 25, USA

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1 solution

Hassan Abdulla
Dec 20, 2017

f ( x ) = { 0 x ∈ Q ′ x x ∈ Q f\left( x \right) =\begin{cases} 0\qquad x\in Q' \\ x\qquad x\in Q \end{cases}

since f(x) continuous only when x=0

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