Show that the function defined by `g (x) = x - [x]` is discontinuous at all integral points. Here [x] denotes the greatest integer less than or equal to x.

Explanation

To show that the function defined by \( g(x) = x - [x] \) is discontinuous at all integral points, we will analyze the function around these points.

### Step-by-Step Solution:

1. **Understanding the Function**:
The function \( g(x) = x - [x] \) represents the fractional part of \( x \). Here, \( [x] \) is the greatest integer less than or equal to \( x \).

2. **Behavior of \( g(x) \)**:
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