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Real function/Identity on Q/Else 0/Continuous in 0/Exercise
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Prove that the function
f
:
R
⟶
R
{\displaystyle f\colon \mathbb {R} \longrightarrow \mathbb {R} }
defined by
f
(
x
)
=
{
x
,
if
x
∈
Q
,
0
,
otherwise
,
{\displaystyle {}f(x)={\begin{cases}x,\,{\text{ if }}x\in \mathbb {Q} \,,\\0,\,{\text{ otherwise}}\,,\end{cases}}\,}
is only at the zero point
0
{\displaystyle {}0}
continuous.
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