# Set of “rounded to nearest p” fixed decimal numbers?

I'm trying to define a set of "fixed precision" or "rounded" numbers. For example, I want to define a rotation in degrees by every $5$ degrees, so $X = \{0,5, \ldots , 355, 360\}$.

$$X = \{x_i \in \Re \mid (x_\min \le x_i \le x_\max) \text{ and } (x_i \mod p = 0)\}$$

$p$ - precision (5)

$x_\min$ - minimum (0)

$x_\max$ - maximum (360)

This occurs frequently in engineering. Is there a name for this type of set? And what about trailing zeroes? In the above, this set would also include $0.00$, $5.00000$, etc., which I want to avoid since the set should have only 73 elements in it!

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"this set would also include 0.00" Stop right there - how is 0.00 different from 0? Also, how do $0^\circ$ and $360^\circ$ differ? –  anon Apr 11 '12 at 20:27
You could call it the image of a finite arithmetic progression, or, in a slight abuse of language, a finite arithmetic progression. This would also include a case like $\{1,6,11,\dotsc\}$, in which the common residue is non-zero. The case of common zero residue could also be called a set of consecutive multiples of $p$. –  joriki Apr 11 '12 at 20:59
Not everything with the word "set" is set theory. –  Asaf Karagila Apr 11 '12 at 21:39
@anon good point, there is no difference between 0.00 and 0 mathematically, but I am using this in a computer algorithm where I do want to track significant figures. So maybe I should be talking about sets of strings? And diff between 0 and 360 rotation might be talking about turns of a screw - but agree this was a confusing choice of example –  DoctorJ Apr 12 '12 at 4:48