Let $a\in \mathbb R$ and $f:\mathbb R\to \mathbb R$ be defined by $f(x) = 1$ when $x > a$, and otherwise $f(x)=0$. Show that $f$ is not continuous at $a$.
This problem is in a section on open balls and neighborhoods. I can show that it's continuous every where other than $a$, but I can't think of a reason it wouldn't be continuous at $a$.
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