Correct set notation with an indexed range

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I have a set of numbers

$$ A_c = \{0,0.25,0.5,0.75,1\} $$

Would it be correct to define this set more generally with the following notation (assuming $x_{max}$, $x_{min}$ and $n$ are defined)?

$$ A_c = \{x_\text{min} + (i-1) \cdot \frac{x_\text{max} - x_\text{min}}{n-1}\}_{i=1}^\text{n} $$

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Assuming you have a set that is $\{k, k + \frac{m-k}n, k + 2\frac {m-k}n, ...., k + (n- 1)\frac {m-k}n, m\}$ That can be written as

$\{k + i\frac {m-k}n| i\in \mathbb Z; 0\le i \le n\}$ which if we let $k = x_{min}$ and $m = x_{max}$ can be written as

$\{x_{min} + i*\frac{x_{max} - x_{min}}n\}_{i=0}^n$

By putting it as

$\{x_\text{min} + (i-1) \cdot \frac{x_\text{max} - x_\text{min}}{n}\}_{i=1}^\text{n}$

you are omitting the final term.