Find the number of points of continuity of $f:\mathbb{R}\rightarrow \mathbb{R}$, where $f(x)=2^{x}$, for $x \in \mathbb{Q}$ and $f(x)=x^3$, for $x \in \mathbb{R}-\mathbb{Q}$.
Finding points of continuity on $\mathbb{Q}$ and $\mathbb{R} - \mathbb{Q}$
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real-analysis
continuity
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0The points of continuity are the points where $2^x=x^3$. I don't manage to find solutions of this. – 2017-02-22
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0And for good reason. One solution is somewhere between $1$ and $2$, the other between $9$ and $10$. But I don't think there's a formula for any of them. This is the kind of equation that usually has either a very simple solution (like an integer) or is impossible to solve analytically. – 2017-02-22