Question

At what point is `f(x) = x - [x]` discontinuous?

Answer 1

I assume that `[x]` is the greatest integer in `x` also known as the floor function.

`x-[x] = 0` for integer `x` and it is the decimal part of `x` for non-integers.

As a consequence of that, the graph of `x-[x]` consists of line segments joining points `(n,0)` with `(n+1, 1)`. Closed at the first point and open at the second.

`x-[x]` is continuous at non-integers (locally linear) and continuous from the right at integers.

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