Question

If `f(x)=[x/3], x in [0, 30]` where [.] denotes Greatest Integer Function , then the discontinuous points of these functions are `x=3, 6, 9, ..., 30`, i.e, when the given function is an integer.But why we did not take the number "0" as a discontinuous pt?

Answer 1

Please see below.

Explanation:

As I mentioned in my comment, below, there isn't just one definition of "discontinuity point". In fact some textbooks don't give a definition.

Speculative answer
The answer given may be (is probably) related to the following:

The domain of `f` is `[0,30]`.

Since `lim_(xrarr0^+)lfloor x/3 rfloor = 0 = lfloor (0)/3 rfloor`,

`f` is continuous from the right at `0` (the domain of `f` is to the right of `0`).

But `lim_(xrarr30^-)lfloor x/3 rfloor = 9 != lfloor ((30))/3 rfloor = 10`,

so, `f` is not continuous from the left at `30` (the domain of `f` is left of `30`.