f(x)=[x] is a step up function . Is it a strictly increasing function for `x in R.`

Explanation

To determine whether the function \( f(x) = [x] \) (the greatest integer function) is strictly increasing for all \( x \in \mathbb{R} \), we will analyze the function step by step.

### Step 1: Define the Function
The greatest integer function \( f(x) = [x] \) returns the largest integer less than or equal to \( x \). For example:
- \( f(0.2) = 0 \)
- \( f(1.5) = 1 \)
- \( f(-1.3) = -2 \)

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